Question

Find the area of the region enclosed by the curves $y^2=x,x=\frac{1}{4},y=0$ and $x=1$, using integration.

Answer 1

Bounded area

= $\underset{1/4}{\overset{1}{\int }}$y dx

= $\underset{1/4}{\overset{1}{\int }}\sqrt{x}$dx

= $\frac{2}{3}[x^{3/2}{]}_{1/4}^1$

= $\frac{2}{3}(1-\frac{1}{8})$ = $\frac{7}{3}\times \frac{7}{8}$ = 7/12 square units