JEE MAIN - Mathematics (2024 - 29th January Evening Shift - No. 22)
Let the area of the region $$\left\{(x, y): 0 \leq x \leq 3,0 \leq y \leq \min \left\{x^2+2,2 x+2\right\}\right\}$$ be A. Then $$12 \mathrm{~A}$$ is equal to __________.
Answer
164
Explanation
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$$\begin{aligned} & y=2 x+2 \\ & A=\int_\limits0^2\left(x^2+2\right) d x+\int_\limits2^3(2 x+2) d x \\ & A=\frac{41}{3} \\ & 12 A=41 \times 4=164 \end{aligned}$$
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