If the area of the region \ (x, y): 0 leq y leq min \ 2 x, 6 x-x 2 \ \ is A , then 12 A is equal to....

Mathematics · Area under the Curves

JEE Main 2024 — 27 January, Shift 2 — Question 22

If the area of the region $\left\{(x, y): 0 \leq y \leq \min \left\{2 x, 6 x-x^{2}\right\}\right\}$ is $A$ , then $12 A$ is equal to....

Numerical answer — enter this value.

We have

$A=\frac{1}{2} \times 4 \times 8+\int_{4}^{6}\left(6 x-x^{2}\right) d x$

$A=\frac{76}{3}$

$12 \mathrm{~A}=304$

Answer key and solution verified before publishing.

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