\( \int_{-\left( \Pi \right)}^{ \Pi } \frac{xsinx}{1+e^{x}} \,dx\)
is
a) 1/2
b) 3/2
c) 2
d) 1
Answer is given as d). Kindly explain.
Well, I think the options are wrong...The answer I'm getting is Π.
Since the integration limits are from "symmetric" x can be replaced with -x.
Add the new integral that results with this replacement to the original integral.
2I=(integral)(xsin(x)) within the same limits.Just carry out this integral to get the answer.