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## Homework Statement

The area under the graph of the function y = cos inverse x on the interval [0; 1] is rotated

about the x-axis to form a solid of revolution.

(a) Write down the volume V of the solid as a denite integral with respect

to x according to the disc/slicing method. Do NOT attempt to evaluate this

integral.

(b) Write down the volume V of the solid as a denite integral with

respect to y according to the shell method.

(c) Using the antiderivative,

Integral y cos y dy = y sin y + cos y + C;

or otherwise, find the volume V of the solid as an exact real number.

## Homework Equations

V=2*PI integral x*f(x) dx

## The Attempt at a Solution

well

(a)V=integral 1 to 0 Pi*cos^-2x^2 dx

(b)V=2PI integral 1 to 0 ycosy dy

(c) i solved it and i got 2PI(PI/2 -1)