`piint_0^(pi/2) cos^2xdx` Each integral represents the volume of a solid. Describe the solid.

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There are (at least) two methods of computing the volume of a solid of revolution . The first of them is the method of disks. In this method we integrate along the axis of revolution and make cross-sections of the solid perpendicular to that axis, which have a form...

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There are (at least) two methods of computing the volume of a solid of revolution. The first of them is the method of disks. In this method we integrate along the axis of revolution and make cross-sections of the solid perpendicular to that axis, which have a form of disks or rings.

The volume of a thin disk is `pi r^2 dx` where `r` is actually is `f(x).` So the volume of a solid is integral of `pi (f(x))^2 dx.`

So the given integral represents the volume of the solid of rotation. Rotation is over x-axis, the solid is bounded by `x=0,` `x=pi/2` and `f(x)=cos(x).`

(the method of shells also gives a solid of revolution with the same volume, but the solid is completely different)

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