Question

The value of the integeral $\int\limits^{1}_{-1}$$\left\{\frac{x^{2015}}{e^{\left|x\right|}\left(x^{2}+cos\,x\right)}+\frac{1}{e^{\left|x\right|}}\right\}$ dx is equal to

• A. 0
• B. $1-e^{-1}$
• C. $2e^{-1}$
• D. $2\left(1-e^{-1}\right)$

Answer 1

Answer: (D)

$\Rightarrow \int\limits^{1}_{-1} \left(odd+\frac{1}{e^{\left|x\right|}}\right)dx$
$= 0+2 \int\limits^{1}_{0} \frac{dx}{e^{x}} = 2\left(1-e^{-1}\right)$