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JEE Advanced2010MathematicsArea Under CurvesActual

Paragraph: Consider the polynomial f(x)=1+2 x+3 x^2+4 x^3 . Let s be the sum of all distinct real roots of f(x) and let t=|s| . Question: The area bounded by the curve y=f(x) and the lines x=0, y=0 and x=t , lies in the interval

Options

  1. A( 3 4 , 3 )
  2. B( 21 64 , 11 16 )
  3. C(9,10)
  4. D(0, 21 64 )

Correct answer

A. ( 3 4 , 3 )

Step-by-step solution

₀^ 1 / 2 f(x) d x gathered = (1+2 x+3 x^2+4 x^3 ) d x =x+x^2+x^3+x^4 ₀^ 1 / 2 f(x) d x= 15 16 > 3 4 ₀^ 3 / 4 f(x) d x= 530 256 < 3 gathered

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