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

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

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Bounded area

= $$\int\limits_{1/4}^1$$y dx

= $$\int\limits_{1/4}^1\sqrt x$$dx

= $$\frac23[x^{3/2}]_{1/4}^1$$

= $$\frac23(1-\frac18)$$ = $$\frac73\times\frac78$$ = 7/12 square units