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NDA2017MathematicsDefinite IntegrationActual

What is ₀^ 2 1+ x 2 d x equal to?

Options

  1. A8
  2. B4
  3. C2
  4. D0

Correct answer

A. 8

Step-by-step solution

aligned & ₀^ 2 1+ x 2 d x & x 2 = 2 ( x 4 )=2 x 4 x 4 aligned aligned & ₀^ 2 ^2 x 4 + ^2 x 4 +2 x 4 x 4 & = ₀^ 2 ( x 4 + x 4 )^2 d x aligned aligned & = ₀^ 2 | x 4 + x 4 | d x=4 [- x 4 + x 4 ]₀^ 2 & =4 [- ( 2 4 - 0 )+ ( 2 4 - 0 ) ] aligned aligned & =4[-(-1)+(1)] & =4 2=8 aligned

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