Question

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

Answer 1

Consider the given curves.

$y=x^3$

$y=x^2$

Area bounded by the these curves

$=\left|{\int }_{x_1}^{x_2}(y_2-y_1)dx\right|$

$=\left|{\int }_1^2(x^2-x^3)dx\right|$

$=|{\left[\frac{x^3}{3}\right]}_1^2-{\left[\frac{x^4}{4}\right]}_1^2|$

$=|\frac{1}{3}(8-1)-\frac{1}{4}(16-1)|$

$=|\frac{7}{3}-\frac{15}{4}|$

$=\left|\frac{28-45}{12}\right|$

$=\frac{17}{12}squnits$

Hence, the area bounded by these curves is $\frac{17}{12}squnits$.