Learn integral calculus—indefinite integrals, Riemann sums, definite integrals, application problems, and more.

Performing u -substitution with definite integrals is very similar to how it's done with indefinite integrals, but with an added step: accounting for the limits of integration. Let's see what this means by finding ∫ …

Learn about antiderivatives and indefinite integrals with Khan Academy's comprehensive video lessons on AP Calculus AB.

The definite integral of a velocity function gives us the displacement. To find the actual distance traveled, we need to use the speed function, which is the absolute value of the velocity.

Since definite integrals are the net area between a curve and the x-axis, we can sometimes use geometric area formulas to find definite integrals. See how it's done.

Definite integrals represent the area under the curve of a function, and Riemann sums help us approximate such areas. The question remains: is there a way to find the exact value of a definite …

Sal evaluates definite integrals of functions given their graphs. He does so using various properties of integrals.

Definite integrals are commonly used to solve motion problems, for example, by reasoning about a moving object's position given information about its velocity. Learn how this is done and about the …

Surface integrals are used anytime you get the sensation of wanting to add a bunch of values associated with points on a surface. This is the two-dimensional analog of line integrals.

Definite integrals represent the area under the curve of a function and above the 𝘹-axis. Learn about the notation we use to write them and see some introductory examples.