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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 2 · Set 2 · Q22
Evaluate: ∫_0^a^3 (x^2)/(x^6+a^6) d x
Evaluate : \[\int_{0}^{a^{3}} \frac{x^{2}}{x^{6}+a^{6}} d x \]
Marking-scheme solution
Put $\displaystyle x^{3}=t \Rightarrow x^{2} d x=\frac{d t}{3}$
Given integral $\displaystyle =\frac{1}{3} \int_{0}^{a^{9}} \frac{d t}{t^{2}+\left(a^{3}\right)^{2}}$
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CBSE Class 12 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.