`x = 2sqrt(y), x = 0, y = 9` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or...

`x = 2sqrt(y), x = 0, y = 9` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. (about the y-axis)

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You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves `x = 2sqrt y, x =0` , the line y = 9, about y axis, using washer method, such that:

`V = int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)`

You need to...

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scisser | Student

`V = pi(int_0^9(x^2) dy)` . Now, the radius of the revolution is x . `x = 2sqrt(y)` , so `x^2 = 4y` . The volume becomes `V = pi (int_0^9(4y) dy) `
`= pi [2y^2]|_0^9 `
`= pi (2(9)^2 - 2(0)^2) `
`= 162 pi. `

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