Question

Find the area of the figure bounded by the following curves
$y$ = $x^3,$ $y=27,x=0$.

Answer 1

$y=x^3,y=27,x=0$.

${\int }_0^{27}xdy={\int }_0^{27}{y}^{\frac{1}{3}}dy$

$=\frac{y^{\frac{1}{3}+1}}{\frac{1}{3}+1}{|}_0^{27}$

$=\frac{3}{4}{y}^{\frac{4}{3}}{|}_0^{27}$

$=\frac{3}{4}(27{)}^{\frac{4}{3}}$

$=\frac{3}{4}(3{)}^{3\times \frac{4}{3}}=\frac{3^5}{4}$

$=\frac{243}{4}$