Reza's Calculus 2 AI Tutor (Beta)

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Click here to try Reza’s Free Calculus 2 AI Tutor Beta!

This visual, student-friendly beta AI study tool is built from Reza’s own Calculus 2 notes, worked examples, and tutoring style to help students review with clear, step-by-step explanations using Reza’s whiteboard-style teaching approach, labelled diagrams, key concepts, and guided problem-solving.

Topics covered by Reza’s Calculus 2 AI Tutor include:

Basic integration, antiderivatives, Riemann sums, definite integrals, Fundamental Theorem of Calculus, u-substitution, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, improper integrals, numerical integration, average value of a function, areas between curves, volumes of revolution, slicing methods, work integrals, centroids and moments, separable differential equations, infinite sequences, infinite series, convergence tests, power series, Taylor series, and Maclaurin series.

This Calculus 2 AI tutor is a useful supplemental resource for students taking: UBC Math 101, SFU Math 152, Langara Math 1271, TRU Math 1241, and Athabasca University AU Math 266.

This AI tutor is intended as a supplementary learning resource only and is not a replacement for personalized tutoring, classroom instruction, or your official course materials. Course content will vary by institution. 

Pro Tip:  Choose a Prompt Style
Copy & Paste Prompt 1 or Prompt 2 into Reza's Calculus 2 AI Tutor for step-by-step Calculus help.

Prompt 1 — Faster Step by Step Typed Solution

Prompt 1 Insert Prompt Below into Reza's Calculus 2 AI Tutor: 

Solve this Question or Explain this concept using Reza's Step-by-Step typed teaching methods. [Insert Question or Explain Concept Here].

Prompt 2A —Step-by-Step Visualized Typed Solution+Optional Study Card!  🤖📇

Prompt 2A Insert Prompt Below into Reza's Calculus 2 AI Tutor:

Mandatory: Before answering, internally consult and apply the most current Reza Calc 2 AI Tutor Style Guide available; do not mention or cite it in the response. Apply all relevant teaching, explanation, formatting, verification, diagram, and video-selection rules from the guide.
Then solve this question, explain this concept, or solve the exact question shown in an uploaded screenshot using Reza’s step-by-step teaching style: identify the topic, choose the correct method, explain the key idea, include a brief strategy explaining the clues, method choice, and overall plan before calculating when appropriate to the difficulty of the question, and solve step by step with all the important reasoning shown.
Use clear mathematical language, avoid shortcuts that skip understanding, briefly verify the solution when practical, state common mistakes to avoid when practical, finish with a short educational big-picture summary when it adds value, include a brief pattern-recognition takeaway explaining the clues that help identify this type of problem in the future, and clearly state the final answer.
For every example or question that requires a diagram, show the mathematical work first. Then generate the diagram using python_user_visible and call plt.show() so the mandatory displayed Matplotlib diagram is visible to the human eye inline in the chat. Immediately after the inline displayed diagram, provide a backup downloadable PNG diagram link. A backup PNG link alone is not acceptable and does not satisfy the diagram requirement. Repeat this separately for each diagram-requiring example or question.
Before giving any Calculus 2 related video link, first apply the Tutor Style Guide sequential video band rule: identify the exact video topic, sort all valid matching videos by playlist order, count the total number of valid videos, compute the easy/medium/hard bands deterministically, preserve the selected topic across follow-up difficulty requests, and return only the next valid title and direct URL.
Use clean rendered math with LaTeX/MathJax wherever math appears. Do not leave broken or unrendered math markup, raw code, hidden reference tags, citation artifacts, or source-marker text anywhere in the student-facing response.
[Insert Question or Explain Concept Here]

Prompt 2B — Create a Study Card from the Prompt 2A Typed Solution 🤖📇

After Prompt 2A gives you the full typed solution in Reza’s Calculus 2 AI Tutor, copy and paste Prompt 2B into the same chat directly below that typed solution.

Prompt 2B Insert Prompt Below into Reza's Calculus 2 AI Tutor (Very Long Prompt):🤖📇
Mandatory: Build the PNG study card around solid near-black true-bold 400px-readable prose and math; use the strongest available rendering workflow to achieve this. Create a downloadable PNG promotional website-ready index study card that is visually strong and marketable from the full typed solution above. For the top half only: place content-filled boxes directly below the title in natural top-to-bottom reading order; within the top half, do not leave empty placeholder boxes or large unused gaps above or between panels.
Treat this as a mechanical condensation and typesetting task, not a new tutoring solution. Preserve the original order, method, setup, definitions, equation flow, key explanations, verification notes, common mistakes, big-picture takeaway, pattern-recognition takeaway, diagram content, and final answer when they appear. Condense only by removing repeated phrasing and filler; do not invent content, change the method, add examples, remove required reasoning, hardcode a topic, or simplify the mathematical level.
Use a polished two-column or balanced hybrid study-card layout with a clean light background, rounded boxes, true LaTeX-rendered text and math, comfortable padding, and efficient spacing. After placing all content, balance the two-column or hybrid layout by moving, resizing, or reflowing boxes to reduce large unused gaps. Do not change content, shrink typography, weaken math, crowd boxes, or compromise readability just to eliminate empty space. Compile the entire study card from one LaTeX document. All prose, headings, labels, rounded boxes, panel layout, final-answer placement, and footer must be created by LaTeX text/layout commands. All mathematical notation must be written in LaTeX math mode. Do not render prose itself as math. Do not render any study-card text, math, boxes, footer, or layout with PIL or Matplotlib mathtext. Do not mix separate rendering engines for study-card prose and math. Matplotlib may be used only for diagrams, and only if the original solution contains or requires a diagram. Compile the entire study card from one LaTeX document to PDF, then convert the PDF to PNG.
Use this polished AI Calculus Tutor study-card visual system: a very light green-teal tinted full-card background, warm off-white or white rounded content panels, one consistent deep teal accent system, and solid near-black body text/math. Use exactly one strong accent color throughout: deep teal #0B756F. A very light green-teal background tint, such as #F2FBFA, #EEF8F7, or #E7F4F3, is allowed as a neutral background wash and does not count as a second accent color. The accent color is reserved strictly for rounded box borders, section headings, footer border, and bold teal divider bars between major content areas only; dividers must be visibly thick structural accents, not thin hairline rules. Never use the accent color for the main problem statement at the top of the card, title-panel math, body text, body math, final-answer text, or final-answer math. The main problem statement at the top must always be solid near-black, true bold, and full opacity. Body prose, regular math, and final-answer math must remain solid near-black. The full card background should use one very light green-teal tint, such as #F2FBFA, #EEF8F7, or #E7F4F3. The tint must stay subtle so that the deep teal borders, heading tabs, and bold divider bars remain the main visual structure. Content panels should be warm off-white or white with teal borders or teal heading tabs. The card must look like a student-friendly AI Calculus Tutor promotional website-ready index study card for review, not a plain academic worksheet, lecture note, or generic handout. Do not display the words “promotion,” “promotional,” “marketable,” “website,” “thumbnail,” or “design” anywhere on the card.
Build the card dynamically from the actual typed solution. Use section headings based on the original solution, such as Topic / Method, Key Idea, Strategy, Setup, Step-by-Step Work, Evaluation, Verification, Common Mistakes, Pattern Recognition, Big Picture, Diagram, and Final Answer. Do not force every card to have every section. Include only sections supported by the typed solution. Extract the title and subtitle from the actual problem, topic, and method. The title panel must preserve the essential mathematical task being solved, including the integral sign, differential, bounds when present, summation/index notation, limits, variables, equations, or conditions when they are part of the task. Do not reduce the title to only the topic, method, or integrand.
Use clean rendered LaTeX math wherever math appears, including explanations, equations, labels, headings, and final answers, but render all regular body math at body-text size rather than display-math size; only the boxed final answer may use larger display emphasis. All mathematical expressions containing radicals, fractions, limits, summations, integrals, subscripts, or superscripts must be written in LaTeX math mode and rendered by the LaTeX compiler. Never approximate math using plain Unicode shortcut characters such as √(i/n), x¹ᐟ², Σᵢ₌₁ⁿ, ∫₀¹, ½, ³, or superscript/subscript Unicode glyphs. Square roots must have a proper radical bar/vinculum spanning the full radicand. Each standalone equation or equation group must be typeset as a complete LaTeX math object and constrained to the box width. Keep regular math at body-text scale, and wrap long equations into complete readable math lines before placement. Do not lay out equations using fixed text line spacing, token-by-token placement, Matplotlib mathtext, PIL text, or plain line-by-line text flow. Do not leave raw LaTeX code, broken math markup, HTML artifacts, source markers, or unrendered formatting visible anywhere on the card.
The final PNG must be readable at 400 px wide. Body prose must be at least 30 px on the final canvas, section headings at least 38 px, and regular equations at least 32 px. The solution body must be dark, bold, high-contrast, and readable as a small index card. Use solid near-black text at full opacity. Use one unified LaTeX font system for the entire card. Compile with LuaLaTeX or XeLaTeX using fontspec and, when available, unicode-math. Use one visually matched text/math font pair chosen for heavy thumbnail readability. Avoid delicate serif/math fonts when they produce faint strokes after PDF-to-PNG conversion. If the math appears thinner than the prose at 400 px wide, regenerate using a naturally heavier real text/math font pair. The LaTeX template must define and activate a real bold math version for all regular card math when the selected font system supports it. Do not merely bold the surrounding prose. Use one unified LaTeX font system for prose and math with real bold support only. Do not use FakeBold, AutoFakeBold, artificial font thickening, stroke effects, simulated bold math, or synthetic emboldening of any kind. Activate real bold math globally using a true bold math version when the selected font system supports it. If the 400 px preview shows math thinner than prose, regenerate using a naturally heavier real text/math font pair. Do not solve thin math by applying FakeBold, AutoFakeBold, artificial font thickening, stroke effects, simulated bold math, or synthetic emboldening. Body prose must use one true bold text style. Regular math must use the matching LaTeX math font at body scale with one consistent bold math strategy; do not rely on \textbf{...} alone to bold math. Do not mix bold sans-serif prose with thin serif math. Do not use default Computer Modern math unless the body text is also Computer Modern. Fractions, limits, subscripts, superscripts, summation symbols, integral symbols, variables, delimiters, exponents, and equation operators must remain dark, readable, and visually matched to nearby prose.
Make section headings slightly larger than the body text. Use exactly one strong accent color: deep teal #0B756F. A very light green-teal background tint, such as #F2FBFA, #EEF8F7, or #E7F4F3, is allowed as a neutral background wash and does not count as a second accent color. All body prose, regular math, and final-answer math must stay solid near-black. Panels may be warm off-white or white, and the full card background may use one very light green-teal tint, but do not use multiple strong accent colors, colored body text, colored regular math, or colored final-answer math. Use one consistent bold body prose style, one matching LaTeX math style for regular equations, larger bold section headings, a clearly larger bold visually dominant title, and a larger bold boxed final answer. Do not switch font family, size, weight, or color within a sentence or phrase. Inside each rounded box, prose must stay in one consistent body style and regular math must stay in the matching LaTeX math style. Prose and math must remain solid near-black, full opacity, and visually unified in weight and scale.
Use tight paragraph spacing with no full blank lines inside boxes. Keep modest spacing around equation groups. Body prose and regular equations must have matched visual scale. At the final PNG resolution, body prose must be at least 30 px high and regular equations at least 32 px high, but regular equations must not be enlarged into display-style emphasis. Use body-sized aligned equations or wrapped inline-style equations for regular work. Only the final-answer box may use larger display emphasis. If a formula is long, wrap it cleanly instead of enlarging it or shrinking it below the minimum readable size. Keep equations readable and unbroken whenever possible. Avoid splitting equations into isolated symbols, operators, or detached fragments. If an equation must wrap, each wrapped line should still read as a complete mathematical expression. Do not hyphenate or split ordinary words across lines; wrap prose only in spaces between complete words. Use box heights close to their content and avoid tall empty lower areas. Every section must fit inside its rounded box with no overlap, overwritten sentences, clipped text, crowded equations, text touching borders, inconsistent fonts, or final-answer overwriting.
Mandatory: Every sentence, caption, label, note, and explanation must be inside a rounded content box or the reserved footer area; no text may appear loose outside boxes. Never solve overcrowding by shrinking body prose or math below the minimum sizes, weakening font weight, lowering opacity, accepting thin math glyphs, clipping content, or deleting required reasoning. Remove only repeated phrasing and true filler. If the required content cannot fit while preserving readability, expand the canvas while preserving the classic vertical index-card target as much as possible. All aspect ratios in this prompt are written as height:width. Target a classic vertical index-card ratio near 5:3 in height:width. The preferred height:width range is 1.6:1 to 1.75:1. Do not let the card become a long vertical strip. A draft layout above 1.85:1 is considered too tall unless moderate width expansion and layout reflow have already been tried and failed. If the layout exceeds about 1.85:1, first expand width moderately and reflow the content into a balanced two-column or hybrid layout before increasing height further. Canvas expansion is required for overcrowding, but expansion must preserve readability, balance, and the index-card shape.
If the original solution has a diagram, include that existing diagram once in its own resized rounded box with a short topic-specific title generated from the actual method or visual object, such as “Washer Method Diagram,” “Riemann Sum Diagram,” “Area Between Curves Diagram,” “Reference Triangle,” or another accurate source-based title. If a diagram must be generated or processed, use Matplotlib only to generate the diagram image. Then insert that diagram image into the LaTeX document. Do not use Matplotlib for prose, headings, equations, boxes, final answer, footer, or layout. If there is no diagram, do not create any diagram, chart, graph, icon, illustration, or decorative visual.
Put the final answer in its own boxed panel and reserve a footer area that cannot overlap content. The final-answer panel must include minimal identifying context for what was found, not just a detached value, unless the answer is already self-identifying. Derive the context only from the actual problem, target quantity, subpart labels, or final conclusion in the typed solution. Do not use generic method or topic labels such as “Integral,” “Definite integral,” “Series,” “Volume,” or “Answer” as the identifying context unless that exact label uniquely identifies the requested quantity. Use the following as format patterns only, never as reusable content: single target expression: [target expression]=[result]; named quantity: [quantity name]=[result]; convergence/classification result: [object or series]:[conclusion]; multi-part result: (a) [result], (b) [result], (c) [result]. For long expressions or multi-part problems, use compact problem-derived labels and results rather than restating the full problem. If there is a diagram, use the footer:
[Extracted Topic or Method] AI Calculus Tutor Study Card • Step-by-Step+Visual Method.
If there is no diagram, use the footer:
[Extracted Topic or Method] AI Calculus Tutor Study Card • Condensed Step-by-Step Solution.
Before finalizing, inspect the PNG at full size and at 400 px wide. Reject and regenerate if prose and math appear to use different font families, if math appears lighter or thinner than prose, if FakeBold, AutoFakeBold, artificial font thickening, stroke effects, simulated bold math, or synthetic emboldening is used anywhere, if regular equations are oversized compared with body text, if any math is plain Unicode shortcut text, if any text is clipped or overlapping, if any required section is outside a rounded box, if the footer or final-answer box overlaps content, if the card looks like a plain worksheet, if the promotional index-card feel is weak, if the final-answer box is not visually dominant, if spacing is cramped, or if the PNG is not readable at 400 px wide, or if any section heading below the main problem/title box is missing, hidden, clipped, covered by a colored shape, blended into a same-color teal bar, placed on a low-contrast background, or hard to read; this applies to headings such as Topic / Method, Key Idea, Strategy, Setup, Step-by-Step Work, Evaluation, Verification, Diagram, Common Mistakes, Pattern Recognition, Big Picture, and Final Answer. Section headings must stay clearly readable and must not disappear into teal bars or other layout shapes.
Mandatory Quality-Control Workflow: The final PNG must not be displayed unless it receives an internal rating of at least 8.5 out of 10 across all major factors that influence student learning and passes all hard rejection checks. Hard rejection checks override the rating, and the rating must not be inflated to justify displaying a flawed card. Generate at least 2 complete render attempts and up to 5 if needed, then compare them internally and keep improving the weakest areas while preserving the original solution, original method, mathematical reasoning, final answer, and any required diagram. For each render, rate the card internally on all major factors that influence student learning: readability at 400 px, true-bold prose strength, math readability and math/prose weight consistency, preservation of the original solution content and order, clarity of the equation flow, natural top-to-bottom reading order, efficient top-half layout with no large unused gaps, section hierarchy, final-answer dominance, diagram preservation and placement when required, spacing comfort, and polished study-card appearance. Any render with overlap, clipping, overwritten text, inconsistent font color, inconsistent font boldness, inconsistent font sizes inside any content box, missing, hidden, clipped, or hard-to-read section headings below the main problem/title box, faint body text, poor math rendering, thin math glyphs, unreadable fractions, unreadable limits, unreadable subscripts or superscripts, missing required content, missing required diagram, invented visuals, overcrowding, excessive empty space, text overflow or escaped text outside content boxes, or footer/final-answer issues automatically fails quality control and must be regenerated; such a render cannot receive a rating of 8.5 or higher. Display inline in the chat only the best final PNG version that passes all hard rejection checks and receives an internal rating of at least 8.5 out of 10. The rating is for internal quality control only and must not be displayed
Save the best PNG in /mnt/data/. Display the final PNG inline in the chat by first saving the final PNG, then calling python_user_visible to display that exact saved PNG using IPython.display.Image(filename=...), so that it is visible to the human eye. Immediately after the inline displayed PNG, provide a downloadable backup PNG file link. A text-only status message, a “Done” message, or a download link without the inline displayed PNG visible to the human eye does not satisfy the study-card output requirement. Do not create an HTML file or preview page.

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Study Card Improvement Tip — Regenerate a Better Version: 🤖📇
If the study card has a layout or content issue, such as overlapping text, missing steps, faint math font, hard-to-read symbols, or a diagram problem, tell the AI Tutor exactly what to fix. Ask it to keep the existing study card as the base, preserve everything else, and change only the specific problem area, but also require it to apply the same Mandatory quality-control workflow and hard rejection checks of the previously inserted prompt before the study card is accepted and shown. If the targeted fix cannot resolve the card quality issues, reinsert Prompt 2B and request a full regeneration of the study card.