JEE MAIN - Mathematics (2024 - 27th January Evening Shift - No. 25)
If the area of the region $$\left\{(x, y): 0 \leq y \leq \min \left\{2 x, 6 x-x^2\right\}\right\}$$ is $$\mathrm{A}$$, then $$12 \mathrm{~A}$$ is equal to ________.
Answer
304
Explanation
We have
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$$\begin{aligned} & A=\frac{1}{2} \times 4 \times 8+\int_\limits4^6\left(6 x-x^2\right) d x \\ & A=\frac{76}{3} \\ & 12 A=304 \end{aligned}$$
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