JEE MAIN - Mathematics (2019 - 9th January Evening Slot - No. 15)
The area of the region
A = {(x, y) : 0 $$ \le $$ y $$ \le $$x |x| + 1 and $$-$$1 $$ \le $$ x $$ \le $$1} in sq. units, is :
A = {(x, y) : 0 $$ \le $$ y $$ \le $$x |x| + 1 and $$-$$1 $$ \le $$ x $$ \le $$1} in sq. units, is :
$${2 \over 3}$$
2
$${4 \over 3}$$
$${1 \over 3}$$
Explanation
_9th_January_Evening_Slot_en_15_1.png)
Required area
$$ = \int\limits_{ - 1}^1 {\left( {x\left| x \right| + 1} \right)} dx$$
$$ = 0 + \left( x \right)_{ - 1}^1 = 2$$
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