Question

The area between two arms of the curve $\left|y\right|=x^3$ from $x=0$ to $x=2$ is

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is C $8$

For the graph of $|y|=f\left(x\right)$ we remove all the branches which are below x axis and reflect all those branches which are above x axis.

y= $x^3$ $x\ge 0$

$-x^3$

Hence we have the graph as shown

And the area of the graph is=${\int }_0^2(x^3-(-x^3))dx$

$={\int }_0^2({2x}^3)dx$

$={\left(\frac{2x^4}{4}\right)}_0^2$

$=8$

So the answer is $\left(C\right)=8$