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JEE Main20244 Apr 2024Evening ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the region described by (x, y): y^2 2 x . , and .y 4 x-1 is

Options

  1. A11 32
  2. B8 9
  3. C11 12
  4. D9 32

Correct answer

D. 9 32

Step-by-step solution

aligned & Shaded area = _ - 1 2 ^1 (x_ Right -x_ Left ) d y & y^2=2 x & y=4 x-1 Solve & y=1, y=- 1 2 & Shaded area = _ - 1 2 ^1 ( y+1 4 - y^2 2 ) d y & = ( 1 4 ( y^2 2 +y )- y^3 6 )_ - 1 2 ^1= 9 32 aligned

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