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NDA2024MathematicsDefinite IntegrationActual

Let 3 f(x)+f ( 1 x )= 1 x +1 What is 8 ₁^2 f(x) d x equal to?

Options

  1. A(8 e )
  2. B(4 e )
  3. C2
  4. D2-1

Correct answer

A. (8 e )

Step-by-step solution

aligned 8 ₁^2 f(x) d x & =8 ₁^2 ( 3 8 x - x 8 + 1 4 ) d x & = ₁^2 ( 3 x -x+2 ) d x & = [3 x- x^2 2 +2 x ]₁^2 & = (3 2- 4 2 +4 )- (3 1- 1 2 +2 ) & =3 2+2- 3 2 = 1 2 +3 2 & = 1 2 e+ 2^3= e + 8 & = (8 e ) aligned

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