# homework

Use the shell method

y=14x-x^2, x=0, y=49

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1. I assume the axis of rotation is the line y=49. So, the shells have thickness dy, and

v = ∫[0,49] 2πrh dy
where r = 49-y and h = (7+√(49-y))-(7-√(49-y))

v = ∫[0,49] 2π(49-y)((7+√(49-y))-(7-√(49-y))) dy = 26891.2π

you can check using discs:

v = ∫[0,14] π(R^2-r^2) dx
where R=49 and r=49-y

v = ∫[0,14] π(49^2-(49-(14x-x^2))^2) dx

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posted by Steve

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