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

2023
Views:

489

Pages:

1
Author:

Karson Orr

Workshop #18 Z 1. Compute x3 dx. 1 − x2 2. Consider the region between the graph of y = x1 and the x-axis, with x ≥ 1. The solid obtained by rotating this region about the x-axis is called Gabriel’s horn. Find the volume of Gabriel’s horn. 3. (a) Find the total area of the four rectangles below. Z 5 1 dx, determine whether or not the result will be larger or 1 x smaller than the area of the four rectangles above. Why? (c) Without actually computing the area, determine if the area of the shaded region below will be larger or smaller than the area of the four rectangles above? Why? (b) Without actually computing (d) Find the area of the shaded region above. Z ∞ 1 4. (a) Compute dx. x5 Z 1∞ 1 (b) Consider dx. Without actually computing this integral, determine if it will be larger or x8 1 smaller than the integral in the previous problem. Why?