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,…
JEE Main 2022 — Mathematics Calculus
2022integerhard
Let S be the region bounded by the curves y=x3 and y2=x. The curve y=2∣x∣ divides S into two regions of areas R1 and R2. If max∣R1,R2∣=R2, then R1R2 is equal to ______
Official previous-year question
Held on 24 Jun 2022 · Verified 6 Jul 2026.
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Solution
Intersection point of {y}^{2}=x&y=2|x| in the first quadrant will be (41,21)
Also, intersection point of y={x}^{3}&{y}^{2}=x in first quadrant will be (1,1)
Area of the region S=∫01(x−x3)dx=[32x23−4x4]10=125
Area of region R1=∫041(x−2x)dx=[32x23−x2]041=481
∴R2=S−R1=4819
So, R1R2=19
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