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Evaluate the definite integralsint0^(pi...

Evaluate the definite integrals`int_0^(pi/2) cos2xdx`

Text Solution

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Consider `I=int _0^(pi/2)cos^2xdx`----------(1)
`I=int_0^(pi/2) cos^2(pi/2-x)dx`
`I=int_0^(pi/2) sin^2xdx`-----(2)
Adding (1) and (2) `2I=int_0^(pi/2) dx`
`2I=(pi/2)-0`
`I=pi/4`
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