Question

The area bounded by the curves $f\left(x\right)=x^3-3x$ and $g\left(x\right)=2x^2$ in the second quadrant is

• A. $\frac{12}{23}$ sq. units
• B. $\frac{7}{12}$ sq. units
• C. $\frac{2}{3}$ sq. units
• D. $\frac{3}{5}$ sq. units

Answer 1

The correct option is B $\frac{7}{12}$ sq. units



Required area
$=\underset{-1}{\overset{0}{\int }}(x^3-3x-2x^2)dx$
$={[\frac{x^4}{4}-\frac{3x^2}{2}-\frac{2x^3}{3}]}_{-1}^0$
$=0-(\frac{1}{4}-\frac{3}{2}+\frac{2}{3})$
$=\frac{7}{12}$ sq. units