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JEE Main202224 Jun 2022Morning ShiftMathematicsArea Under CurvesActual

Let S be the region bounded by the curves y = x 3 and y 2 = x . The curve y = 2 x divides S into two regions of areas R 1 and R 2 . If max R 1 , R 2 = R 2 , then R 2 R 1 is equal to ______

Correct answer

0

Step-by-step solution

Intersection point of y 2 = x   &   y = 2 x in the first quadrant will be 1 4 , 1 2 Also, intersection point of y = x 3   &   y 2 = x in first quadrant will be 1 , 1 Area of the region S = ∫ 0 1 ( x - x 3 ) d x = 2 x 3 2 3 - x 4 4 1 0 = 5 12 Area of region R 1 = ∫ 0 1 4 x - 2 x d x = 2 x 3 2 3 - x 2 0 1 4 = 1 48 ∴    R 2 = S - R 1 = 19 48 So, R 2 R 1 = 19

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