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Evaluate: int(-pi//2)^(pi//2) sqrt(cosx-...

Evaluate: `int_(-pi//2)^(pi//2) sqrt(cosx-cos^3x) dx`

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`I=int_(-pi//2)(pi//2)ubrace(sqrt(cosx-cos^(3)x)dx)_(f(x))`
`2int_(0)^(pi/2)sqrt(cosx-cos^(3)x) dx` (as `f(x)` is an even function)
`=2int_(0)^(pi//2) sqrt(cosx sin^(2)x) dx`
`=2int_(0)^(pi//2)sqrt(cosx) sin xdx`
`=2[-((cosx)^(3//2))/(3//2)]_(0)^(pi/2)`
`=2xx2/3`
`=4/3`
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