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

2023
Views:

431

Pages:

1
Author:

Trevon Carney

Workshop #5 Note: If your class is doing Techniques of Integration before Volumes, skip to problem number 4. 1. The region bounded by the graphs of y = 2 + Find the volume of the resulting solid. √ x, y = 2 − x, and x = 1 is rotated about the x-axis. 2. The region bounded by the graphs of f (x) = ln x, y = 1, the x-axis, and the y-axis is rotated about the y-axis. Find the volume of the resulting solid using the disk method. (Hint: Use horizontal rectangles.) 3. The region bounded by the graphs of y = ln x and the lines y = x, y = 0, and y = 2 is rotated about the y-axis. Find the volume of the resulting solid. 4. Integrate the following. Z 1 dx (a) 2 − 5x Z π 4 (b) (1 + tan x) sec2 x dx 0 Z √ 1 + cot x dx (c) sin2 x 5. Each of the following integrals represents the area of a region between two curves. Sketch the region. Z e (a) (1 − ln x) dx 1 Z 3 2 (b) (7 − 2x) − dx 3 x−1 2 6. Consider the region bounded by the graphs of y = ln x, y = 1, y = 2, and x = 0. (a) Set up a dx integral that computes the area of this region. (b) Set up a dy integral that computes the area of this region.