Integral Calculus Simulations
A collection of interactive 3D visualizations and simulations to help you master concepts in integral calculus.
Antiderivatives and Indefinite Integrals - Theory & Concepts
Understanding antiderivatives, indefinite integral notation, basic integration formulas, and properties of linearity.
Simulation: Family of Antiderivatives
Legend
Observe how adjusting the constant C shifts the curve vertically without altering its shape or instantaneous slope.
Definite Integrals - Theory & Concepts
Understanding Riemann sums, the Fundamental Theorem of Calculus, properties of definite integrals, and improper integrals.
Simulation: Riemann Sums & Area
Area Analysis
As $n \to \infty$, the width $\Delta x \to 0$, and the Riemann sum converges precisely to the definite integral.
Techniques of Integration - Theory & Concepts
Mastering methods for evaluating complex integrals: u-substitution, integration by parts, trigonometric integrals, and partial fractions.
Interactive Lab: Integration by Parts (LIATE)
LIATE Priority List
The function type highest on this list should be selected as u.
Which part should be u?Select the function based on the LIATE rule.
Applications of Integration - Theory & Concepts
Exploring the applications of definite integrals: finding the area between curves, calculating the volume of solids of revolution, determining arc length, finding the center of mass, fluid pressure, work, and surface area.
Area Between Curves Visualizer
The shaded region represents the area where f(x) ≥ g(x).
Multiple Integrals - Theory & Concepts
Extending the concept of integration to functions of two or three variables: evaluating double and triple integrals, changing coordinate systems, and exploring their applications.
Double Integral & Volume Visualizer
Increase resolution to see the Riemann sum converge to the exact volume. Note: High resolution may affect performance.