** 20.T Integration by parts
**

** Reference:** Stewart 7.1

** Keywords: ** Integration by parts, reduction formula

** Learning Objectives:** The student will be able to:

- Apply the method of integration by parts to evaluate both definite and indefinite integrals
- Recognize the types of integrals to which integration by parts applies
- Derive the method of integration by parts from the product rule

**Note:** We will try to start on volumes this day, too.

** 20.R Volumes I **

** Reference:** Stewart 5.2, 5.3

** Keywords: ** Volume, solid of revolution, method of slicing,
disks and washers, cylindrical shells

** Learning Objectives:** The student will be able to:

- Set up a definite integral to compute the volume of a solid whose
cross-sectional area
*A(x)*is known:*V = [integral]*(the method of slicing)_{a}^{b}A(x) dx - Apply the method of slicing to solids of revolution, obtaining the method of disks and of washers
- Compute the volume of a solid of revolution by the method of cylindrical shells