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

2023
Views:

445

Pages:

1
Author:

ueffenv0k

Workshop #6 1 1. The region bounded by the graphs of y = (1 − x2 ) 2 and y = 1 − x is rotated about the y-axis. Find the volume of this region by the shell method. 1 2. The region bounded by the graphs of f (x) = x 2 and g(x) = x3 is rotated about the y-axis. Find the volume of this region using the shell method. 3. The region bounded by the graphs of y = x2 , y = x − 1, y = 0, and y = 2 is rotated about the x-axis. Find the volume of this region using the shell method. 4. The region bounded by the graphs of y = ex , y = 1, and x = 1 is rotated about the x-axis. (a) Set up the integrals to find the volume of this region by both the disk method and by the shell method. (b) Compute one of these integrals. πx 5. The region bounded by the graphs of y = 2 sin and y = x, between x = 0 and x = 1 is rotated 2 about the y-axis. Set up an integral to compute the volume. 6. The following integral represents the volume of a solid that is obtained by rotating a region in the x − y plane about one of the coordinate axes. Z V =π 2 x4 dx 0 (a) If this was a region that was rotated about the x-axis, then what was the region? (b) If this was a region that was rotated about the y-axis, then what was the region?