Question

Let $\alpha$ be the area of the larger region bounded by the curve $y^2=8 x$ and the lines $y=x$ and $x=2$, which lies in the first quadrant Then the value of $3 \alpha$ is equal to _____

Answer 1

The correct answer is 22.

y=x
& y2=8x
Solving it
x2=8x
∴x=0,8
∴y=0,8
x=2 will intersect occur at
y2=16⇒y=±4
∴ Area of shaded
=2∫8​(8x​−x)dx=2∫8​(22​x​−x)dx
=[22​⋅3/2x3/2​−2x2​]08​
=(342​​⋅20/2−32)−(342​​⋅20/2−2)
=3128​−32−316​+2=3112−90​=322​=A
∴3A=22