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  4. Area bounded by y = x3, y = 8 and x = 0 is

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Q. Area bounded by $y = x^3, y = 8$ and $x = 0 $ is

KCETKCET 2015Application of Integrals

Solution:

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Required area $=\int\limits_{0}^{8} x \,d y $
$=\int\limits_{0}^{8} y^{1 / 3} d y $
$=\frac{3}{4}\left[y^{4 / 3}\right]_{0}^{8}=\frac{3}{4}\left(8^{4 / 3}\right) $
$=\frac{3}{4} \times 16=12$ sq units