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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 4 · Set 3 · Q11
Evaluate: ∫_-3^3 (x^4)/(1+e^x) d x
Evaluate : \[\int_{-3}^{3} \frac{x^{4}}{1+e^{x}} d x \]
Marking-scheme solution
Let, \(\displaystyle I=\int_{-3}^{3} \frac{x^{4}}{1+e^{x}} d x\)
\(\displaystyle I=\int_{-3}^{3} \frac{x^{4}}{1+e^{-x}} d x\) (using property)
\[=\int_{-3}^{3} \frac{e^{x} x^{4}}{1+e^{x}} d x
\]
Adding equations ($\displaystyle 1$) and
\[2 I=\int_{-3}^{3} \frac{x^{4}\left(1+e^{x}\right)}{1+e^{x}} d x
\]
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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.