Section 5.3: Evaluating Definite Integrals Practice HW from Stewart Textbook (not to hand in) p. 374 # 1-27 odd, 31-43 odd.

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Section 5.3: Evaluating Definite Integrals Practice HW from Stewart Textbook (not to hand in) p. 374 # 1-27 odd, odd

Definite Integral The definite integral is an integral of the form This integral is read as the integral from a to b of. The numbers a and b are said to be the limits of integration. For our problems, a < b. Definite Integrals are evaluated using The Fundamental Theorem of Calculus.

Fundamental Theorem of Calculus Let be a continuous function for and be an antiderivative of. Then

Example 1: Evaluate. Solution:

Example 2: Evaluate. Solution:

Additional Integration Formulas 1. 2.

3. 4.

Example 3: Evaluate Solution:

Example 4: Evaluate Solution:

Example 5: Evaluate Solution:

Recall that if for. Then Definite Integral:

Example 6: Find the area under the graph of on [0, 2]. Solution:

Example 7: Evaluate Solution:

Note For a function f (x) that is both positive and negative over an interval, the total area is the area enclosed by the negative part of the curve minus the negative part of the curve.

Example 8: Consider the function over the interval. The graph of the function over this interval is given by

Find the total area enclosed between the function and the x axis. Solution: