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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_{-1}^1\left( e ^{x^3}+ e ^{-x^3}\right)\left( e ^x- e ^{-x}\right) d x$ is equal to
  • A
    $\frac{ e ^2}{2}-2 e$
  • B
    $e^2-2 e$
  • ✓
    $0$
  • D
    $2 e ^{-2}-2 e$
✓

Answer

Correct option: C.
$0$
(C)
Let $f (x)=\left( e ^{x^3}+ e ^{-x^3}\right)\left( e ^x- e ^{-x}\right)$
$\therefore \quad f (-x)=\left( e ^{-x^3}+ e ^{x^3}\right)\left( e ^{-x}- e ^x\right)$
$=-\left( e ^{x^3}+ e ^{-x^3}\right)\left( e ^x- e ^{-x}\right)=- f (x)$
$\therefore f (x)$ is an odd function.
$\therefore \quad \int_{-1}^1\left(e^{x^3}+e^{-x^3}\right)\left(e^x-e^{-x}\right) d x=0$

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