Let the area of the bounded region \ (x, y): 0 leq 9 x leq .y 2 , y geq 3 x-6 \ be A . Then 6 A is equal to \ \ \ \ .

Mathematics · Area under the Curves

JEE Main 2025 — 8 April, Evening Shift — Question 45

Let the area of the bounded region $\{(x, y): 0 \leq 9 x \leq$ $\left.y^{2}, y \geq 3 x-6\right\}$ be $A$ . Then $6 A$ is equal to $\_\_\_\_$ .

Numerical answer — enter this value.

The given problem has area bounded $\rightarrow \infty$

However, if we correct in to $y^{2} \leq 4 x$ then here is the solution.

Required area $=\int_{-3}^{3}\left(\frac{y+6}{3}-\frac{y^{2}}{9}\right) d y$

$=\frac{27}{2}$ sq. units

Answer key and solution verified before publishing.

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