JEE MAIN - Mathematics (2021 - 25th July Morning Shift - No. 8)
The area (in sq. units) of the region, given by the set $$\{ (x,y) \in R \times R|x \ge 0,2{x^2} \le y \le 4 - 2x\} $$ is :
$${8 \over 3}$$
$${{17} \over 3}$$
$${{13} \over 3}$$
$${7 \over 3}$$
Explanation
_25th_July_Morning_Shift_en_8_1.png)
Required area = $$\left. {\int\limits_0^1 {\left( {4 - 2x - 2{x^2}} \right)dx = 4x - {x^2} - {{2{x^3}} \over 3}} } \right|_0^1$$
$$ = 4 - 1 - {2 \over 3} = {7 \over 3}$$
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