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  • Let  be the region bounded by the curves <img alt="\mathrm{y=x^{3}}" src="https://entrancecorner

Let  \mathrm{S} be the region bounded by the curves \mathrm{y=x^{3}} and \mathrm{y^{2}=x}.  The curve \mathrm{y=2|x|}  divides \mathrm{S} into two regions of areas  \mathrm{\mathrm{R}_{1} \; and\; \mathrm{R}_{2}}.
\mathrm{If \: \max \left\{R_{1}, R_{2}\right\}=R_{2}, \; then \; \frac{R_{2}}{R_{1}}} is equal to ________.

Option: 1

19


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

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

\mathrm{R_{1}= \int_{0}^{\frac{1}{4}}\left ( \sqrt{x}-2x \right )dx= \frac{1}{48}}
\mathrm{R_{2}= \frac{5}{12}-\frac{1}{48}= \frac{19}{48}}

\mathrm{\therefore \frac{R_{2}}{R_{1}}=19}

Posted by

Deependra Verma

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