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 =

Question

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 $\frac{R_{2}}{R_{1}} =$

Smart Achievers · Accepted Answer

(19)

$= \int_{0}^{1} \sqrt{x} d x - \frac{3}{4}$

$= {[\frac{2 x^{3 / 2}}{3} - \frac{x^{4}}{4}]}_{1}^{0} = \frac{5}{12}$

$R_{1} = \int_{0}^{1 / 4} (\sqrt{x} - 2 x) d x$

$= {[\frac{2 x^{3 / 2}}{3} - x^{2}]}_{0}^{1 / 4} = \frac{1}{48}$

$∴$ $R_{2} = \frac{19}{48}$

$So, \frac{R_{2}}{R_{1}} = 19$

Solution

Q.
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 $\frac{R_{2}}{R_{1}} =$

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Solution

Q. 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 R2R1=

Ans. (19) =∫01xdx-34 =[2x3/23-x44]10=512 R1=∫01/4(x-2x)dx =[2x3/23-x2]01/4=148 ∴ R2=1948 So, R2R1=19

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Q.
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 $\frac{R_{2}}{R_{1}} =$