Unit 5 - Objective 5 - Definite Integral

The Definite Integral

"the integral of f(x) form a to b, with respect to x"

The definite integral was defined on the last worksheet as the limit of and to evaluate the definite integral we used the Fundamental Theorem of Calculus.

For ease, we let F(x) be the antiderivative where C=0. Even if we use C, it would subtract out anyway.

Note: If f(x) is positive for all x in the interval from a to b, then this definite integral is exactly the area under the curve and above the x-axis.

To find the value of the definite integral, find the antiderivative first (just like the indefinite integral), then evaluate the antiderivative at the "upper limit, b, and subtract the value of the antiderivative at the "lower limit", a. The definite integral is a number. The indefinite integral was a function.

Try it!

Problem 1:

Problem 2: