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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Definite Integration

BITSAT 2014 · Mathematics · Definite Integration

∫_ 0 ^ 10 x^ 10 (10-x)^ 10 +x^ 10 d x is equal to

∫010x10(10−x)10+x10dx\int_{0}^{10} \frac{x^{10}}{(10-x)^{10}+x^{10}} d x is equal to

Options

  1. A10
  2. B5
  3. C2
  4. D10\frac{1}{0}

Correct answer

B. 5

Step-by-step solution

Let I=∫010x10(10−x)10+x10dxI=\int_{0}^{10} \frac{x^{10}}{(10-x)^{10}+x^{10}} d x...(1) I=∫010(10−x)10(10−x)10+x10dxI=\int_{0}^{10} \frac{(10-x)^{10}}{(10-x)^{10}+x^{10}} d x...(2) Adding (1) and (2), we get 2I=∫010dx⇒2I=10⇒I=52 I=\int_{0}^{10} d x \Rightarrow 2 I=10 \Rightarrow I=5
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