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AP EAMCET201822 Apr 2018Morning ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the region bounded by the X -axis and the curve y=1-x-6 x^2 is

Options

  1. A125 216
  2. B125 512
  3. C25 216
  4. D25 512

Correct answer

A. 125 216

Step-by-step solution

We have, aligned & y=1-x-6 x^2 & y=- [6 x^2+x-1 ] & y=-6 [x^2+ x 6 - 1 6 ] & y=-6 [ (x+ 1 12 )^2- 1 144 - 1 6 ] & y=-6 (x+ 1 12 )^2+ 1 24 +1 & y=-6 (x+ 1 12 )^2+ 25 24 & 6 (x+ 1 12 )^2=- (y- 25 24 ) & (x+ 1 12 )^2=- 1 6 (y- 25 24 ) & aligned aligned & Required area = _ -1 / 2 ^ 1 / 3 y d x & = _ -1 / 2 ^ 1 / 3 (1-x-6 x^2 ) d x= [x- x^2 2 -2 x^3 ]_ -1 / 2 ^ 1 / 3 & = ( 1 3 - 1 18 - 2 27 )- (- 1 2 - 1 8 + 1 4 ) & = ( 18-3-4 54 )- ( -4-1+2 8 ) & = 11 54 + 3 8 = 44+81 216 = 125 216 sq unit aligned

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