JEE MAIN - Mathematics (2020 - 8th January Evening Slot - No. 16)
The area (in sq. units) of the region
{(x,y) $$ \in $$ R2 : x2 $$ \le $$ y $$ \le $$ 3 – 2x}, is :
{(x,y) $$ \in $$ R2 : x2 $$ \le $$ y $$ \le $$ 3 – 2x}, is :
$${{34} \over 3}$$
$${{29} \over 3}$$
$${{31} \over 3}$$
$${{32} \over 3}$$
Explanation
_8th_January_Evening_Slot_en_16_1.png)
x2 $$ \le $$ y $$ \le $$ – 2x + 3
$$ \Rightarrow $$ x2 = – 2x + 3
$$ \Rightarrow $$ x2 + 2x – 3 = 0
$$ \Rightarrow $$ (x + 3) (x – 1) = 0
$$ \Rightarrow $$ x = – 3, x = 1
Area = $$\int\limits_{ - 3}^1 {\left( { - 2x + 3 - {x^2}} \right)dx} $$
= $$\left( { - {x^2} + 3x - {{{x^3}} \over 3}} \right)_{ - 3}^1$$
= $$\left( { - 1 + 3 - {1 \over 3} + 9 + 9 - 9} \right)$$
= 11 - $${{1 \over 3}}$$
= $${{{32} \over 3}}$$ sq. unit
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