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COMEDK2017MathematicsDefinite Integration

Evaluate ₀^ / 2 x ( x 2 + x 2 )³ d x .

Options

  1. A2- 2
  2. B2+ 2
  3. C3+ 3
  4. D3- 3

Correct answer

A. 2- 2

Step-by-step solution

We have, = ₀^ / 2 x 2 - x 2 ( x 2 + x 2 )² d x Put x 2 + x 2 =t 1 2 (- x 2 + x 2 ) d x=d t Also, when x=0 t=1 When x= 2 t= 2 aligned I &= ₁^ 2 2 d t t² &=2 [- 1 t ]₁^ 2 =2 [- 1 2 +1 ]=(2- 2 ) aligned

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