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BITSAT2020MathematicsArea Under CurvesActual

The line y=m x bisects the area enclosed by lines x=0, y =0 and x =3 / 2 and the curve y =1+4 x - x ² Then the value of m is

Options

  1. A13 6
  2. B13 2
  3. C13 5
  4. D13 7

Correct answer

A. 13 6

Step-by-step solution

y=1+4 x-x²=5-(x-2)² We have ₀^ 3 / 2 (1+4 x-x² ) dx =2 ₀^ 3 / 2 mx dx = 3 2 +2 ( 9 4 )- 1 3 ( 27 8 )= m 9 4 On solving we get m = 13 6

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