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  4. The area enclosed between the graph of y = x3 and the lines x = 0, y = 1, y = 8 is

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Q. The area enclosed between the graph of $y = x^{3}$ and the lines $x = 0$, $y = 1$, $y = 8$ is

Application of Integrals

Solution:

Given curve is $y = x^{3}$
or $x = y^{1 /3}$
image
$\therefore \quad$ Required area$=\int\limits_{1}^{8} y^{1/ 3}\, dy=\left[\frac{y^{4 /3}}{4 /3}\right]_{1}^{8}$
$=\frac{3}{4}\left[8^{4 /3}-1^{4/ 3}\right]$
$=\frac{3}{4}\times\left(16-1\right)$
$=\frac{3}{4}\times15$
$=\frac{45}{4}$ sq. units