Lucas S.

asked • 12/01/23

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=x3, y=1, x=2; about y=-3


Doug C.

Seems like another boundary is required (likely y = 0)? If that is the case, the washer method requires two integrals. Using the shell method is probably easier. desmos.com/calculator/djbzehfoqj
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12/01/23

1 Expert Answer

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Bradford T. answered • 12/01/23

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Retired Engineer / Upper level math instructor

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The hardest part about volume of rotation problems is setting up the integral.

Use the washer method


V=π∫21(r1)2-(r2)2dx

r1 = y-y0 = x3-(-3) = x3+3

r2 = 1-(-3) = 4

V= π∫21(x3+3)2-42dx = π∫21x6+6x3-7dx


You should be able to do the integration


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