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QJEEM24Ma39d7: JEE Main 2024 Mathematics - Class 12 JEEM24Ma39d7 Solution: Let the area of the region be , where and are coprime numbers.…

Let the area of the region {(x,y):x−2y+4⩾0,x+2y2⩾0,x+4y2≤8,y⩾0}\left\{(x, y): x-2 y+4 \geqslant 0, x+2 y^2 \geqslant 0, x+4 y^2 \leq 8, y \geqslant 0\right\} be mn\frac{\mathrm{m}}{\mathrm{n}} , where m\mathrm{m} and n\mathrm{n} are coprime numbers. Then m+n\mathrm{m}+\mathrm{n} is equal to _____________.

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JEE Main 2024 (Online) 27th January Morning Shift Mathematics - Area Under The Curves Question 29 English Explanation

A=∫01[(8−4y2)−(−2y2)]dy+∫13/2[(8−4y2)−(2y−4)]dy=[8y−2y33]01+[12y−y2−4y33]13/2=10712=mn∴m+n=119

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