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

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 and indefinite integrals are connected by the Fundamental Theorem of Calculus. It says that to calculate a definite integral (the area between two bounds), you have to find the …

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.

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 …

And we wanna evaluate the definite integral from negative four to zero of f of x, dx. And like always, pause this video and see if you can work through this. Now when you first do this you …

Riemann sums help us approximate definite integrals, but they also help us formally define definite integrals. Learn how this is achieved and how we can move between the …

We can use a definite integral in terms of 𝘺 to find the horizontal area between curves of two functions of 𝘺.

This video shows how to find the overlapping area between two circles using definite integrals and a graphing calculator. It demonstrates entering the integral function, specifying the variable, …

To find it exactly, we can divide the area into infinite rectangles of infinitely small width and sum their areas—calculus is great for working with infinite things! This idea is actually quite rich, …