`x = sqrt(sin(y)), 0<=y<=pi, x = 0` (a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. (about y = 4) (b) Use your calculator to evaluate the integral correct to five decimal places.

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Let's use the method of cylindrical shells.

The parameter for a cylinder will be `y` from `y=0` to `y=pi.`

The radius of a cylinder (the distance to the axis of rotation) is `4-y,`

the height of a cylinder is `sqrt(sin(y)).`

The volume is `2pi int_0^pi (4-y)sqrt(sin(y)) dy.`

I believe "calculator"...

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Let's use the method of cylindrical shells.

The parameter for a cylinder will be `y` from `y=0` to `y=pi.`

The radius of a cylinder (the distance to the axis of rotation) is `4-y,`

the height of a cylinder is `sqrt(sin(y)).`

The volume is `2pi int_0^pi (4-y)sqrt(sin(y)) dy.`

I believe "calculator" means "computer algebra system" here. WolframAlpha says the answer is 36.57476.

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