The integral represents the volume of a solid. Describe the solid. \pi\int_{0}^{1}(y^{4}-y^{8})dy a) The integral describes the volume of the solid ob

e1s2kat26 2021-05-17 Answered
The integral represents the volume of a solid. Describe the solid.
π01(y4y8)dy
a) The integral describes the volume of the solid obtained by rotating the region R={{x, y}|0y1, y4xy2} of the xy-plane about the x-axis.
b) The integral describes the volume of the solid obtained by rotating the region R={{x, y}|0y1, y2xy4} of the xy-plane about the x-axis.
c) The integral describes the volume of the solid obtained by rotating the region R={{x, y}|0y1, y4xy2} of the xy-plane about the y-axis.
d) The integral describes the volume of the solid obtained by rotating the region R={{x, y}|0y1, y2xy4} of the xy-plane about the y-axis.
e) The integral describes the volume of the solid obtained by rotating the region R={{x, y}|0y1, y4xy8} of the xy-plane about the y-axis.
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Expert Answer

Yusuf Keller
Answered 2021-05-18 Author has 90 answers

Step 1
π01(y4y8) dy=1
d1=π[(y2)2(y4)2] dy
Axis of solution =yaxis
upper boundary x=y2
lower boundary x=y4
region in x-y plane
y4<x<y2
0y1
Answer: (c)

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