Q72 / 125 · BITSAT 2014 · Mathematics

$\int_{0}^{10} \frac{x^{10}}{(10-x)^{10}+x^{10}} d x$ is equal to

  • A
    10
  • Correct answer
    B
    5
  • C
    2
  • D
    $\frac{1}{0}$

Solution

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

Hence, the correct answer is option: 'B'.

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