Question

The area of the region (in the square unit) bounded by the curve $x ^ { 2 } = 4 y$ line $x = 2$ and x-axis is

• A. 1
• B. $\frac { 2 } { 3 }$
• C. $\frac { 4 } { 3 }$
• D. $\frac { 8 } { 3 }$

Answer 1

Answer: (B)

$\frac { 2 } { 3 }$

Answer 2

Given $x ^ { 2 } = 4 y$

Shaded area

$= \int _ { 0 } ^ { 2 } \frac { x ^ { 2 } } { 4 } d x$ $= \frac { 1 } { 12 } \left[ x ^ { 3 } \right] _ { 0 } ^ { 2 } = \frac { 8 } { 12 } = \frac { 2 } { 3 }$ .