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

The basic idea of Integral calculus is finding the area under a curve. To find it exactly, we can divide the area into infinite rectangles of infinitely small width and sum their areas—calculus is …

Practice Functions defined by definite integrals (accumulation functions) Get 3 of 4 questions to level up!

We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together …

Learn AP®︎ Calculus AB—everything you need to know about limits, derivatives, and integrals to pass the AP® test.

Functions defined by definite integrals (accumulation functions) Finding derivative with fundamental theorem of calculus Finding derivative with fundamental theorem of calculus: …

Integrals that are inverse trigonometric functions ∫ 1 a 2 x 2 d x = arcsin (x a) + C ∫ 1 a 2 + x 2 d x = 1 a arctan (x a) + C

Functions defined by definite integrals (accumulation functions) Finding derivative with fundamental theorem of calculus Finding derivative with fundamental theorem of calculus: …

There are many ways to extend the idea of integration to multiple dimensions: some examples include Line integrals, double integrals, triple integrals, and surface 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.