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JEE Main2011MathematicsDefinite IntegrationActual

The value of ₀^1 8 (1+x) 1+x^2 d x is

Options

  1. A8 2
  2. B2 2
  3. C2
  4. D2

Correct answer

D. 2

Step-by-step solution

I =8 ₀^1 (1+ x ) 1+ x ^2 dx =8 ₀^ 4 (1+ ) 1+ ^2 ^2 d ( let x= )=8 ₀^ 4 (1+ ( 4 - ) ) d =8 ₀^ 4 (1+ 1- 1+ ) d =8 ₀^ 4 2 d -8 ₀^ 4 (1+ ) d =8 2 4 -I2 I =2 2 I = 2

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