By Eric Lake

5.3: The Fundamental Theorem of Calculus

This page covers the Fundamental Theorem of Calculus Part 2--the one you use most of all to evaluate definite integrals.

This module has both videos and a practice worksheet at the bottom!

Videos

An introduction to the Fundamental Theorem of Calculus (Part 2), which we use to evaluate definite integrals, along with an example.

A definite integral involving a product. Remember, don't split integrals across multiplication.

A definite integral of a simple fraction.

A definite integral with a trigonometric form. We use the unit circle to evaluate the trig function at the bounds.

A definite integral with a form that becomes arctangent, as well evaluating arctangent at those bounds.

A definite integral of a quotient, where we split the fraction across the numerator.

A definite integral of an absolute value, which isn't on our antiderivative chart!

Why we can flip the bounds on a definite integral and get a negative sign, using the FTC.

Worksheet

For your practice, here's a worksheet with eight definite integrals you can work on. Do your best to do these without looking notes or a video, at least until you get stuck, then take a look at those resources.

When you are finished, check your work with the full worked out solutions.