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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
The value of $\int_0^1 \ x^2 \ e^x \ d x$ is equal to
  • ✓
    e - 2
  • B
    e + 2
  • C
    $e^2-2$
  • D
    $e ^2$
✓

Answer

Correct option: A.
e - 2
(A)
$\int_0^1 x^2 e ^x d x=\left[x^2 \cdot e ^x\right]_0^1-\int_0^1 2 x e ^x d x$
$\begin{array}{l}= e -2\left[x e ^x- e ^x\right]_0^1 \\ = e -2[ e - e -(0-1)]= e -2\end{array}$

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