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JEE Main2002MathematicsDefinite IntegrationActual

If y=f(x) makes +v e intercept of 2 and 0 unit on x and y axes and encloses an area of 3 / 4 square unit with the axes then ₀^2 x f^ (x) d x ~~is

Options

  1. A3/2
  2. B1
  3. C5/4
  4. D-3/4

Correct answer

D. -3/4

Step-by-step solution

We have ₀^2 f(x) d x= 3 4 ; Now, ₀^2 x f^ (x) d x=x ₀^2 f^ (x) d x- ₀^2 f(x) d x=[x f(x)]₀^2- 3 4 =2 f(2)- 3 4 =0- 3 4 ( f(2)=0)=- 3 4

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