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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 4 · Set 1 · Q6
Evaluate: ∫_0^1 x^2 e^x d x
Evaluate : \[\int_{0}^{1} x^{2} e^{x} d x \]
Marking-scheme solution
\[\begin{aligned}
\int_{0}^{1} x^{2} e^{x} d x & =\left[x^{2} e^{x}\right]_{0}^{1}-\int_{0}^{1} 2 x e^{x} d x \\
& =\left[x^{2} e^{x}-2 x e^{x}+2 e^{x}\right]_{0}^{1} \\
& =e-2
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.