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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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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

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Find the area enclosed by the curves y=x^2, x=1/4, y=0 and x=1, using integration.
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