Evaluate the following integral: int0^(p...

Evaluate the following integral: `int_0^(pi//2)(cos x)/(1+sin^2x)dx`

Text Solution

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Given,`int_0^(pi//2)(cos x)/(1+sin^2x)dx`
Put sinx=t and cosxdx=dt.
[x=0⇒t=0] and` [x=π/2⇒t=1]`
. `I=int_0^1 dt/(1+t^2)`
`=[tan^(−1)t]_0^1 =tan^(−1)(x/a)+C`
`=π/4−0`
. `=π/4`.

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