How do you find the volume of the solid if the region in the first quadrant bounded by the curves

auto23652im 2022-07-05 Answered
How do you find the volume of the solid if the region in the first quadrant bounded by the curves x = y y 2 and the y axis is revolved about the y axis?
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Answers (1)

lydalaszq
Answered 2022-07-06 Author has 11 answers
The curve x = y y 2 is a parabola that opens to the left. It has y intercepts 0 and 1
Using discs, we see that the radius is x or y y 2 , the thickness is dy, so the volume or a representative disc is
π r 2 d 9 y = π ( y y 2 ) 2 d y
Integrate from y=0 to y=1
0 1 π ( y y 2 ) 2 d y = π 0 1 ( y 2 3 y 3 + y 4 ) d y
Which I believe is 17 π 60

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