Plot the region R enclosed by y = cos(3x); y = cos(x); x = 0; x = pi Find all relevant intersection points. Find the volume of the solid S obtained by rotating the region R about the axis y = -1.
You need to determine the inner and the outer radius such that:
inner radius: `r(x) = -1 - cos(3x)`
outer radius: `R(x) = -1 - cos x`
You need to evaluate the cross sectional area such that:
`A(x) = pi(R^2(x) - r^2(x))`
`A(x) = pi((-1 - cos x)^2 - (-1 - cos 3x)^2)`
`A(x) = pi(1 + 2cos x + cos^2 x - 1 - 2cos 3x - cos^2 3x)`
You need to evaluate the volume of solid of revolution such that:
`V(x) = int_0^(pi)...
(The entire section contains 249 words.)
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