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]ab A(x) dx
(the method of slicing)
- 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