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.
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