Evaluate : int(0)^(pi//2) (cosx)/((1+sin...

Evaluate : `int_(0)^(pi//2) (cosx)/((1+sin x)(2+sinx)) dx`

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To evaluate the integral \[ I = \int_{0}^{\frac{\pi}{2}} \frac{\cos x}{(1 + \sin x)(2 + \sin x)} \, dx, \] we will use substitution and properties of logarithms. ...

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int_(0)^( pi/2)(cosx)/(1+sin x)dx

int_(0)^( pi/2)(cosx)/(1+sinx)dx

Knowledge Check

int_(0)^(pi//2)(cosx)/((1+sin^(2)x))dx=?

A

`(pi)/(2)`

B

`(pi)/(4)`

C

`pi`

D

none of these

int_(0)^(pi//2) (cosx )/ (1+sin^(2)x)dx=

A

`(-pi)/2`

B

`pi/2`

C

`(-pi)/4`

D

`pi/4`

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