Q70 / 160 · WBJEE 2012 · Mathematics

The value of the integral $\int_{-2}^{2}(1+2 \sin x) e^{|x|} d x$ is equal to

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

Solution

$\int_{-2}^{2}(1+2 \sin x) e^{|x|} d x$ $=\int_{-2}^{2} e^{|x|} d x+2 \int_{-2}^{2} \sin x e^{|x|} d x$ (Since, first function is even and second function is odd). $=2 \int_{0}^{2} e^{|x|} d x+2 \text{ instead of ,} 0=2\left[e^{|x|}\right]_{0}^{2}=2\left(e^{2}-1\right)$

Hence, the correct answer is option: 'C'.

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