University:
San Diego State University
Course:
MATH 151 | Calculus II
Academic year:

2023
Views:

188

Pages:

1
Author:

Allioniy9p

Workshop #16 1. Compute each of the following integrals or show that it diverges. Z ∞ x (a) dx ex 0 Z π 1 dx (b) 2x cos 0 Z 2 ln(2 − x) dx (c) 0 2. Consider the region below the graph of y = e−x , above the x-axis, and to the right of the y-axis. (a) If this region is rotated about the x-axis, what is the resulting volume? (b) If this region is rotated about the y-axis, what is the resulting volume? Z ∞ 3. Consider the integral xn dx. 1 (a) Find a value for n so that this integral would diverge. (b) Find a value for n so that this integral would converge. (c) Find all values of n for which this integral would diverge. Z 1 4. Consider the integral xn dx. 0 (a) Find a value for n so that this integral would diverge. (b) Find a value for n so that this integral would converge. (c) Find all values of n for which this integral would diverge.