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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
$\int(\text{x}-1)\text{e}^{-\text{x}}\text{ dx}$ is equal to:
  • ✓
    $-\text{x}\text{e}^{\text{x}}+\text{C}$
  • B
    $\text{x}\text{e}^{\text{x}}+\text{C}$
  • C
    $-\text{x}\text{e}^{-\text{x}}+\text{C}$
  • D
    $\text{x}\text{e}^{-\text{x}}+\text{C}$
✓

Answer

Correct option: A.
$-\text{x}\text{e}^{\text{x}}+\text{C}$
$\int(\text{x}-1)\text{e}^{-\text{x}}\text{ dx}$
$=(\text{x}-1)\int\text{e}^{-\text{x}}\text{ dx}-\int\Big(\Big[\frac{\text{d}(\text{x}-1)}{\text{dx}}\Big]\int\text{e}^{-\text{x}}\text{dx}\Big)\text{ dx}$
$=(\text{x}-1)\frac{\text{e}^{-\text{x}}}{-1}-\int\frac{\text{e}^{-\text{x}}}{-1}\text{ dx}$
$=-(\text{x}-1)\text{e}^{-\text{x}}+\frac{\text{e}^{-\text{x}}}{-1}+\text{C}$
$=-\text{x}\text{e}^{-\text{x}}+\text{e}^{-\text{x}}+\text{C}$
$=-\text{x}\text{e}^{-\text{x}}+\text{C}$

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