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
(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.
V=2*PI integral x*f(x) dx
The Attempt at a Solution
(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)