1.

The value of the definite integral `int_(0)^(3pi//4)(1+x)sin x+(1-x) cos x)dx` isA. `2 tan (3pi)/(8)`B. `2 tan (pi)/(4)`C. `2 tan (pi)/(8)`D. 0

Answer» Correct Answer - 1
`I= overset(3pi//4)underset(0)int (sinx +cos x) dx+overset(3pi//4)underset(0)int x(sin x-cos x)dx`
`=overset(3pi//4)underset(0)int(sin x+ cos x) dx + x(cos x sin x)_(0)^(3pi//4)`
`+overset(3pi//4)underset(0)int (sin x+ cos x) dx`


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