Question

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

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

Answer 1

Answer: (B)

$y_1$ and $y_2$, we get $x=0,-1,3$
$\text{ Required area }=\underset{-1}{\overset{0}{\int }}\left(y_1-y_2\right)dx=\underset{-1}{\overset{0}{\int }}\left(x^3-3x-2x^2\right)dx$
$={\left(\frac{x^4}{4}-\frac{3x^2}{2}-\frac{2x^3}{3}\right)}_{-1}^0$
$=0-\left(\frac{1}{4}-\frac{3}{2}+\frac{2}{3}\right)=-\left(\frac{3-18+8}{12}\right)=\frac{7}{12}.$