Find value of following definite inte...

Find value of following definite integrals: `int_(-pi/4)^(npi-pi/4)|sin+cosx|dx\ (n in N)`

A

0

B

2n

C

`2sqrt2n`

D

none of these

Verified by Experts

The correct Answer is:

C

`int_(-pi//4)^(npi-(pi)/4)abs(sinx+cosx)=sqrt2int_(-pi//4)^(npi-(pi)/4)abs(sin(x+(pi)/4))dx`

`x+pi/4=trArrdx=dt`
`=sqrt2int_(0)^(npi)abs(sint)dx=nsqrt2int_(0)^(pi)sintdt`
`=nsqrt2(-cos)_(0)^(pi)=nsqrt2(1-(-1))`
`=2sqrt2n`

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