Question

What is the area (in square units) bounded by the curve $y^2 = x$ and the line $x - 4 = 0$?

• A. 30/3 sq. units
• B. 31/3 sq. units
• C. 32/3 sq. units
• D. 29/3 sq. units

Answer 1

Answer: (C)

32/3 sq. units

Answer 2

The area bounded by $y^2 = x$ and $x = 4$ is found by integrating the difference between the right boundary ($x=4$) and the left boundary ($x=y^2$) with respect to $y$, from $y=-2$ to $y=2$.

$A = \int_{-2}^{2} (4 - y^2) dy = \left[ 4y - \frac{y^3}{3} \right]_{-2}^{2} = \left( 8 - \frac{8}{3} \right) - \left( -8 + \frac{8}{3} \right) = 16 - \frac{16}{3} = \frac{32}{3}$.