Question-27 The value of the integral \int_{-a}^{a} \frac{e^{x}}{1+e^{z}} d x is
A) a/4
B) a
C)
e^{-a^{2}}D) a/2
Answer: B) a
Explanation
\int_{-a}^a\frac{e^z}{1+e^z}dx=\int_0^a\left(\frac{e^z}{1+e^e}+\frac{e^{-z}}{1+e^{-z}}\right)dx \left(\because\int_{-a}^af(x)dx=\int_0^a(f(x)+f(-x))dx\right) =\int_0^a\left(\frac{e^z}{1+e^z}+\frac1{1+e^e}\right)dx =\int_0^adx=a