1.

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

Answer»

0
2n
`2sqrt2n`
None of these

Solution :`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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