# calculus

Find the volume of the solid obtained by rotating the region bounded by y=x and y=√x about the line x=2.
Volume =

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1. intersection:
√x = x
x = x^2
x = 0 or x = 1

V = π∫ (2-√x)^2 - (2-x)^2 dy from y = 0 to 1
expand, integrate, etc

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Reiny
2. Now, you may be asking yourself, "Self, how can I integrate
∫ (2-√x)^2 dy ?"
You just need to express x as a function of y. That makes the volume
v = π∫[0,1] (2-y^2)^2 - (2-y)^2 dy = 8π/15

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oobleck
3. Thanks for the correction, oobleck

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Reiny

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