JEE Main 2022 (Online) 26th July Morning ShiftQuestion 1
The odd natural number $a$, such that the area of the region bounded by $y=1$, $y=3$, $x=0$, $x=y^a$ is $\frac{364}{3}$, is equal to :
Application of Integrals
Solution
Area $=\int_1^3y^a\,dy=\frac{3^{a+1}-1}{a+1}=\frac{364}{3}$. $a=5$: $\frac{729-1}{6}=\frac{364}{3}$ (and $a=3$ gives $20$, $a=7$ gives $820$, $a=9$ gives $5904.9$). So $a=5$. Option (B).