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  4. The area bounded by the curve y = x2 , the y -axis and the straight lines y = 1 and y = 4 is

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Q. The area bounded by the curve $ y = x^{2} $ , the $ y $ -axis and the straight lines $ y = 1 $ and $ y = 4 $ is

J & K CETJ & K CET 2016Application of Integrals

Solution:

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Required area
$= \int_{1}^{4} \sqrt{y} dy = \left[\frac{2y^{3/2}}{3}\right]_{1}^{4} $
$ = \frac{2}{3}\left[8-1\right] = \frac{14}{3}$ sq. units