JEE Main 2022 Mathematics - Class 12 JEEM22Ma0b54 Solution: Let S be the region bounded by the curves y = x 3 and y 2 = x.…

QJEEM22Ma0b54: JEE Main 2022 Mathematics - Class 12 JEEM22Ma0b54 Solution: Let S be the region bounded by the curves y = x 3 and y 2 = x.…

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, R₂. If max {R₁, R₂} = R₂, then ${{{R_2}} \over {{R_1}}}$ is equal to ______________.

Step-by-Step Verified Solution

JEE Main 2022 (Online) 24th June Morning Shift Mathematics - Area Under The Curves Question 70 English Explanation

C_{1}: y=x^{3}

C_{2}: y^{2}=x

and

C_{3}=y=2|x|

C_{1}

and

C_{2}

intersect at

(1,1)

C_{2}

and

C_{3}

intersect at

\left(\frac{1}{4}, \frac{1}{2}\right)

Clearly

R_{1}=\int_{0}^{1 / 4}(\sqrt{x}-2 x) d x=\frac{2}{3}\left(\frac{1}{8}\right)-\frac{1}{16}=\frac{1}{48}

and

R_{1}+R_{2}=\int_{0}^{1}\left(\sqrt{x}-x^{3}\right) d x=\frac{2}{3}-\frac{1}{4}=\frac{5}{12}

So,

\frac{R_{1}+R_{2}}{R_{1}}=\frac{5 / 12}{1 / 48} \Rightarrow 1+\frac{R_{2}}{R_{1}}=20

\Rightarrow \frac{R_{2}}{R_{1}}=19

QJEEM22Ma0b54: JEE Main 2022 Mathematics - Class 12 JEEM22Ma0b54 Solution: Let S be the region bounded by the curves y = x 3 and y 2 = x.…

Step-by-Step Verified Solution

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