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Evaluate the definite integrals int0p...

Evaluate the definite integrals `int0pi/4(sinx+cosx)/(9+16sin2x)dx`

A

`1/20 log3`

B

`1/40 log3`

C

`1/20 log 6`

D

`10 log 3`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int_(0)^(pi//4)(sinx+cosx)/(25-16(sinx+cosx)^(2)) dx`
Let `sinx-cosx=t`
`:.I=int_(-1)^(0)(dt)/(25-16t^(2))`
`=1/16int_(-1)^(0)(dt)/((5/4)^(2)-t^(2))`
`=1/16 . 1/2 . 5/4 log [|(5/4+t)/(5/4-t)|]_(-1)^(0)`
`=1/40[log1-"log"1/9]`
`=(log 9)/40`
`=1/20 log 3`
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  15. If f(x) is continuous for all real values of x , then sum(r=1)^nf(r-1...

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  17. f(x) is a continuous function for all real values of x and satisfies i...

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