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Math 142 Worksheet 6
Show all work for full credit. (4 points each)
1. Sketch the region enclosed by the curves and find its area.
a. x = 2y 2 , y = − 12 x + 2
b. y = x2 , y = 2x + 3
c. y = sin x, y = cos x, x = 0, x =
3π
4
1
2
2.
Find the volume of the solid obtained by rotating the region bounded by the given
curves about the given line. Sketch the region, the solid, and a typical disk.
a. y = 2 sin(x), y = 0, x = 0, x = π, rotated about the x-axis
b. x =
√
y + 3, x = 0, y = 6 rotated about the y-axis
c. y = x2 , y = 0, x = 3 rotated about the line x = 3
3
3.
Find the volume of the solid obtained by rotating the region bounded by the given
curves about the given line. Sketch the region, the solid, and a typical washer.
a. y = 3x − x2 , y = x rotated about the x-axis
b. x = y 2 + 1, y = 3 − x about the y-axis
4
4. Find the volume of the solid obtained by rotating the region bounded by x = y 2 and
y = x2 about the given line. Sketch the region, the solid, and a typical washer.
a. about the line x = −1.
b. about the line y = −1.