Question

Find the area of the region bounded by the curve $y=x^3$ from, $x=2$ and $x=4$.

• A. $64$ sq. units
• B. $60$ sq. units
• C. $16$ sq. units
• D. $256$ sq. units

Answer 1

The correct option is B $60$ sq. units

If we draw the graph of $y=x^3$ and find out the region whose area is to be found, then it looks as shown below in the figure.


Area $A={\int }_2^{4}ydx={\int }_2^4\left(x^3\right)dx$
$={\int }_2^4\left(x^3\right)dx={\left(\frac{x^4}{4}\right)}_2^4=(\frac{4^4}{4}-\frac{2^4}{4})$
$=60$ sq. units