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# I keep getting C when the answer is B...calc ab problem?

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- 2 days agoFavorite Answer
Find the volume of the cylinder of radius 2 and height 8

pi * 2^2 * 8 =>

32 * pi

Now remove the solid of revolution formed by y = x^3 , x = 2 and the x-axis

y = x^3

y^(1/3) = x

pi * f(y)^2 * dy , y = 0 , y = 8

Integrate

pi * int(y^(2/3) * dy , y = 0 , y = 8)

pi * (1/(1 + 2/3)) * y^(2/3 + 1) + C =>

pi * (1/(5/3)) * y^(5/3) + C =>

(3pi / 5) * y^(5/3) + C

(3pi/5) * (8^(5/3) - 0^(5/3)) =>

(3pi/5) * (32 - 0) =>

(3pi/5) * 32 =>

(3/5) * 32 * pi

32 * pi - 32 * pi * (3/5) =>

32 * pi * (1 - 3/5) =>

32 * pi * (2/5) =>

64 * pi / 5

What you keep finding is the solid bound by x = -2 , x = 2 and y = 8. We're removing that from a cylinder (kind of scooping it out, as it were) and taking the remaining bit.

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