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NDA2019MathematicsDefinite IntegrationActual

Paragraph: Consider the integrals I ₁= ₀^x x d x 1+ x and I ₂= ₀^ ( -x) d x 1- ( +x) Question: What is the value of I₁ ?

Options

  1. A0
  2. B2
  3. C2

Correct answer

C. 2

Step-by-step solution

aligned & I₁= ₀^ x d x 1+ x = ₀^ -x 1+ ( -x) d x & I₁= ₀^ -x 1+ x d x & 2₁= ₀^ 1+ x d x & I₁= 2 ₀^ 1 1+ ( 2 -x ) d x & I₁= 2 ₀^ 1 1+2 ^2 ( 4 - x 2 )-1 d x aligned aligned & I₁= 2 ₀^ ^2 ( 4 - x 2 ) d x & I₁= 2 [ ( 4 - x 2 ) -1 ]₀^ & I₁= - 2 (-1-1)= aligned

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