int(-pi//4)^(n pi - pi/4) | sin x + cos ...

`int_(-pi//4)^(n pi - pi/4) | sin x + cos x | dx ( n in N) ` is :

A

0

B

2n

C

`2sqrt2n`

D

None of these

Verified by Experts

The correct Answer is:

C

`int_(-pi//4)^(npi -pi/4) |sinx+cosx| = sqrt2 int_(-pi//4)^(npi -pi/4) |sin (x+pi/4)|dx `

` x + pi/4 =t rArr dx = dt`
` = sqrt2 int_0^(n pi)|sin t|dx = n sqrt2 int_0^pi sin t dt `
` = n sqrt2 (-cos t)_0^pi = n sqrt2(1-(-1))`
` = 2sqrt2 n`

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