Question

The area in square units bounded by the curves $y=x^3,y=x^2$ and the ordinates $x=1,x=2$ is

• A. $\frac{17}{12}$
• B. $\frac{12}{13}$
• C. $\frac{2}{7}$
• D. $\frac{7}{2}$

Answer 1

Answer: (A)

$\frac{17}{12}$

The given curves are $y=x^3$ and $y=x^2$

And the limits of $x$ are $x=1,x=2$

Then, the required area is
$A={\int }_1^2(x^3-x^2)dx$
$={\int }_1^2{x}^{3}dx-{\int }_1^2{x}^{2}dx$
$={\left[\frac{x^4}{4}\right]}_1^2-{\left[\frac{x^3}{3}\right]}_1^2$
$=(\frac{16}{4}-\frac{1}{4})-(\frac{8}{3}-\frac{1}{3})$
$=\frac{15}{4}-\frac{7}{3}=\frac{17}{12}$ sq units