Question

Find the area of the region bounded by $y=x^3,y=0,x=2$ and $x=4$.

• A. 64
• B. 60
• C. 16
• D. 256

Answer 1

The correct option is B 60

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 $A={\int }_1^{4}ydx={\int }_2^4\left(x^3\right)dx$
$={\int }_2^4\left(x^3\right)dx={\left(\frac{x^4}{4}\right)}_2^4=(\frac{4^4}{4}-\frac{2^4}{4})=60$