section 5.5 (and 5.7)

SECTION 5.5 (AND 5.7)

Integration by Substitution & Natural Logs

The Chain Rule & Integration• How do we handle something like this?

• Think back to how we took the derivative of a composite function like . . .

-Substitution

Example 1Find the indefinite integral and check the result by differentiation.

Example 2Find the indefinite integral and check the result by differentiation.

Example 3Find the indefinite integral and check the result by differentiation.

What about some of our other trig fnc.’s?• Can we use some of these methods to integrate

something like what we have below?

What about some of our other trig fnc.’s?• Can we use some of these methods to integrate

something like what we have below?

Example 4Find the indefinite integral and check the result by differentiation.

Example 5Find the indefinite integral and check the result by differentiation.

Example 6Find the indefinite integral and check the result by differentiation.

Example 7Find the indefinite integral and check the result by differentiation.

Example 8Find the indefinite integral and check the result by differentiation.

Example 9Find the indefinite integral and check the result by differentiation.

Example 10Evaluate the definite integral.

Example 11Evaluate the definite integral.