# Area bounded by the curve

Question:

Area bounded by the curve $y=x^{3}$, the $x$-axis and the ordinates $x=-2$ and $x=1$ is

A. $-9$

B. $-\frac{15}{4}$

C. $\frac{15}{4}$

D. $\frac{17}{4}$

Solution:

Required Area $=\left|\int_{-2}^{0} y d x\right|+\int_{0}^{1} y d x$

$=\left|\int_{-2}^{0} x^{3} d x\right|+\int_{0}^{1} x^{3} d x$

$=\left|\left[\frac{x^{4}}{4}\right]_{-2}^{0}\right|+\left[\frac{x^{4}}{4}\right]_{0}^{1}$

$=\left|\left[0-\frac{16}{4}\right]\right|+\left[\frac{1}{4}-0\right]$

$=|-4|+\frac{1}{4}$

$=4+\frac{1}{4}$

$=\frac{17}{4}$ sq. units

Thus, the correct answer is D.