volume using cross-sections

Calculus
Tutor: None Selected Time limit: 1 Day

May 18th, 2015

y = 3*sqrt(x) and y=6 intersect at x=4. So the limits of integration are from x=0 to x=4.

External radius r_ext(x) = 6, internal r_int = 3*sqrt(x).

So the volume is
pi*int_from_0_to_4[r_ext^2(x) - r_int^2(x)]dx =

pi*int_from_0_to_4(36 - 9x)dx =
9*pi*int_0_4(4 - x)dx =
9pi*(4x - x^2/2)_0_4 =
9pi*(16-0 - (4^2/2-0)) = 9pi*8 = 72pi.

May 18th, 2015

thank you very much!!!

May 18th, 2015

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