Application of Integrals: The area of the region R=\(x,y):xyle27,\ 1le yle x^2\ is equal to : | JEE Main 2026

JEE Main 2026 (Online) 5th April Morning ShiftQuestion 1

The area of the region $R=\{(x,y):xy\le27,\ 1\le y\le x^{2}\}$ is equal to :

Application of Integrals

$78\log_{e}3-\frac{52}{3}$$54\log_{e}3-\frac{52}{3}$✓ Correct answer$54\log_{e}3-\frac{26}{3}$$54\log_{e}3+\frac{26}{3}$

Solution

For $x>0$: $1\le y$, $\sqrt y\le x\le\frac{27}{y}$, which needs $y\le9$. Area $=\int_1^9\left(\frac{27}y-\sqrt y\right)dy=27\log_e9-\frac23(27-1)=54\log_e3-\frac{52}3$.

Application of Integrals - JEE Mathematics question (JEE Main 2026 (Online) 5th April Morning Shift)

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