Evaluate the integral I=int(0)^(pi//4)...

Evaluate the integral
`I=int_(0)^(pi//4) (sinx+cosx)/(9+16sin2x)`dx

Text Solution

Verified by Experts

The correct Answer is:

`(1)/(20)ln 3`

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int_(0)^(pi//4)(sinx+cosx)/(3+sin2x)dx=

Evaluate the integral int_(0)^(pi//2) (dx)/(4+5cosx )

Knowledge Check

int_(0)^(pi/4) (sinx + cosx)/(3+sin2x) dx=

A

`(1)/(2) log 3`

B

`log 2`

C

`log 3`

D

`(1)/(4) log 3`

int_(0)^(pi//4)(sinx+cosx)/(7+9sin2x)dx=

A

`(log3)/(4)`

B

`(log3)/(36)`

C

`(log7)/(12)`

D

`(log7)/(24)`

int_(0)^(pi//4)(sinx + cos x)/(7+9 sin 2x) dx =

A

`(log 3)/(4)`

B

`(log 3)/(36)`

C

`(log 7)/(12)`

D

`(log 7)/(24)`

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DEFINITE INTEGRALS-Exercise -7(b)

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