Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. a) y = 2 - ²x, y = 0, x = 1, x = 2; about the x-axis b) x = 2√√y, x = 0, y = 9; about the y-axis 3 c) y = x³, y = x, x > 0; about the x-axis d) y² = x, x = 2y; about the y-axis e) y = x, y=√x; about y = 1

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Find the volume of the solid obtained by rotating the region bounded by the given
curves about the specified line. Sketch the region, the solid, and a typical disk or
washer.
1
a) y = 2 - x, y = 0, x = 1, x = 2; about the x-axis
2
b) x = 2√√y, x = 0, y = 9; about the y-axis
c) y = x³, y = x, x>0; about the x-axis
d) y² = x, x = 2y; about the y-axis
e) y = x, y = √x; about y = 1
Transcribed Image Text:Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. 1 a) y = 2 - x, y = 0, x = 1, x = 2; about the x-axis 2 b) x = 2√√y, x = 0, y = 9; about the y-axis c) y = x³, y = x, x>0; about the x-axis d) y² = x, x = 2y; about the y-axis e) y = x, y = √x; about y = 1
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