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Prove that the equality int(0)^(pi//2) s...

Prove that the equality `int_(0)^(pi//2) sin ^(m) x dx = int_(0)^(pi//2) cos ^(m) ` x dx and apply the obtained result in computing the following integrals :
`int_(0)^(pi//2) cos^(2) "x dx and " int_(0)^(pi//2) sin ^(2) x dx`

Text Solution

Verified by Experts

The correct Answer is:
`I = (pi)/(4)`
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