Question

The area in the first quadrant bounded by y = 4x², x = 0 y = 1, and y = 4 is

• A. 2 sq. union
• B. 2$\frac { 1 } { 2 }$ sq. union
• C. 2 $\frac { 1 } { 3 }$ sq. union
• D. 3 sq. union

Answer 1

Answer: (C)

2 $\frac { 1 } { 3 }$ sq. union

Answer 2

Required area = $\int _ { 1 } ^ { 4 } x d y$

= $\int _ { 1 } ^ { 4 } \frac { \sqrt { y } } { 2 } d y$ =$\frac { 1 } { 3 } \left[ 4 ^ { 3 / 2 } - 1 \right]$=2 $\frac { 1 } { 3 }$ sq. units