JEE MAIN - Mathematics (2021 - 26th August Morning Shift - No. 16)
The area of the region $$S = \{ (x,y):3{x^2} \le 4y \le 6x + 24\} $$ is ____________.
Answer
27
Explanation
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For A & B
3x2 = 6x + 24 $$\Rightarrow$$ x2 $$-$$ 2x $$-$$ 8 = 0
$$\Rightarrow$$ x = $$-$$2, 4
Area $$ = \int\limits_{ - 2}^4 {\left( {{3 \over 2}x + 6 - {3 \over 4}{x^2}} \right)dx} $$
$$ = \left[ {{{3{x^2}} \over 4} + 6x - {{{x^3}} \over 4}} \right]_{ - 2}^4 = 27$$
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