JEE Main 2022 · 30 Jul · Shift 2 · Mathematics Q85

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MathematicsInteger+4 / -1Question 85 of 90

If the area enclosed by the curves $y=x^2$ , $y^3=x$ , $x=-1$ and $y=x^2$ , $y^3=x$ , $x=1$ , above the line $x=2y$ is $\dfrac n{n+1}$ , then n is equal to _______.

Your answer

Answer and worked solution

Official answer: 47

Total between $y=x^2$ and $y=x^{1/3}$ : $\frac{13}{12}$ on $[-1,0]$ and $\frac5{12}$ on $[0,1]$ , 1.5 in all.

Below $y=\frac x2$ we lose $\int_0^{1/2}\left(\frac x2-x^2\right)dx=\frac1{48}$ and $\int_{-1}^0\left(\frac x2-x^{1/3}\right)dx=\frac12$ .

Area $1.5-\frac12-\frac1{48}=\frac{47}{48}$ , so $n=47$ .

Answer: 47

Topics:Area between curves

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JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 85