The value of the definite integral `int_(0)^(3pi//4)(1+x)sin x+(1-x) cos x)dx` is

Options

A. `2 tan ((3pi)/8)`
B. `2 tan (pi)/(4)`
C. `2 tan (pi)/(8)`
D. 0

Answer

1

Explanation

`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`