Question

The area(in sq.units) bounded by the curve $y=x^3,x-$ axis and the two ordinates $x=-2,x=1$ is

• A. $9$
• B. $\frac{15}{4}$
• C. $\frac{17}{4}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{17}{4}$


$=\left|\underset{-2}{\overset{0}{\int }}ydx\right|+\underset{0}{\overset{1}{\int }}ydx=\left|\underset{-2}{\overset{0}{\int }}{x}^{3}dx\right|+\underset{0}{\overset{1}{\int }}{x}^{3}dx={\left|\left[\frac{x^4}{4}\right]\right|}_{-2}^0+{\left[\frac{x^4}{4}\right]}_0^1=|-4|+\left[\frac{1}{4}\right]$
$=4+\frac{1}{4}=\frac{17}{4}$sq. units