Dr. Andy Loveless

Dr. Loveless Curiosity Lab

Math 125 Visuals

Calculus II visuals, interactives, and videos organized by section group.

Start with a question. Build a visual. Let the math help explain what is going on.

This page organizes Math 125 into topic chunks. Each section page will eventually collect Desmos visuals, selected videos, short explanations, and questions students can explore.

Back to Course Visual Galleries

How to use this page

Choose the section group you are studying. Each page will eventually include visuals and videos designed to help you see accumulation, area, volume, work, approximation, and infinite processes.

The goal is to make Calculus II feel less like a list of techniques and more like a collection of stories about measuring, adding, slicing, approximating, and modeling.

Math 125 Section Groups

These pages are skeletons for now. Each will become a collection of visuals, interactives, videos, and guiding questions.

Sections 4.9, 5.1, 5.2

Antiderivatives, Area, and the Definite Integral

Accumulation, signed area, Riemann sums, definite integrals, and the transition from adding rectangles to measuring total change.

Question: How does adding tiny pieces measure total change?
Area Riemann Sums Integrals
Open section page →

Sections 5.3, 5.4, 5.5

FTC, Substitution, and Net Change

The Fundamental Theorem of Calculus, accumulation functions, substitution, and interpreting integrals as total change in a story.

Question: How are derivatives and integrals two sides of the same story?
FTC Substitution Net Change
Open section page →

Sections 6.1, 6.2, 6.3

Area, Volume, and Shells

Areas between curves, volumes by slicing, disks, washers, and cylindrical shells as different ways to add up geometric pieces.

Question: What pieces are we adding to build a shape?
Area Volumes Shells
Open section page →

Sections 6.4, 6.5

Work and Average Value

Work, force, distance, springs, pumping, average value, and integrals as a way of combining many small contributions.

Question: How do we add changing effort over changing distance?
Work Average Value Applications
Open section page →

Sections 7.1, 7.2

Integration by Parts and Trig Integrals

New integration tools for products and trigonometric powers, with visual and algebraic ways to understand when each method helps.

Question: What structure tells us which integration tool to try?
Parts Trig Techniques
Open section page →

Sections 7.3, 7.4

Trig Substitution and Partial Fractions

Trigonometric substitution, algebraic decomposition, and choosing substitutions based on hidden geometric or algebraic structure.

Question: What hidden shape or factorization is the integral asking us to see?
Trig Sub Fractions Algebra
Open section page →

Sections 7.5, 7.7, 7.8

Integration Strategy and Improper Integrals

Choosing methods, combining techniques, limits of integration, infinite intervals, vertical asymptotes, and convergence of improper integrals.

Question: What happens when area stretches forever?
Strategy Improper Convergence
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Sections 8.1 and 8.3

Arc Length and Center of Mass

Measuring curve length, adding small distances, and extending calculus ideas to curves described in different ways.

Question: How do we measure the length of a curved path?
Arc Length Center of Mass
Open section page →

Sections 9.1, 9.3, 9.4

Separable Differential Equations

Differential equations, slope fields, separation of variables, exponential growth and decay, Newton’s law of cooling, and other models where a rate depends on the current state.

Question: How can a rule for change tell the story of a whole function?
Diff Eq Separable Models
Open section page →