JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 1
If the area of the region enclosed by the curve $y=x^{2}$ and the line $y=ax$ is $36$ sq. units, then $|a|$ is equal to $\_\_\_\_\_\_$ .
Application of Integrals
Answer$6$
Solution
$x^2=ax\Rightarrow x=0,a$. Area $=\left|\int_0^a(ax-x^2)dx\right|=\frac{|a|^3}6=36\Rightarrow|a|^3=216\Rightarrow|a|=6$.