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Question: Answered & Verified by Expert
$\int_{0}^{10} \frac{x^{10}}{(10-x)^{10}+x^{10}} d x$ is equal to
MathematicsDefinite IntegrationBITSATBITSAT 2014
Options:
  • A 10
  • B 5
  • C 2
  • D $\frac{1}{0}$
Solution:
2717 Upvotes Verified Answer
The correct answer is: 5
Let $I=\int_{0}^{10} \frac{x^{10}}{(10-x)^{10}+x^{10}} d x$...(1)

$I=\int_{0}^{10} \frac{(10-x)^{10}}{(10-x)^{10}+x^{10}} d x$...(2)

Adding

(1) and (2), we get

$2 I=\int_{0}^{10} d x \Rightarrow 2 I=10 \Rightarrow I=5$

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