Question

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

• A. $-9$
• B. $\frac{-15}{4}$
• C. $\frac{15}{4}$
• D. $\frac{17}{4}$

Answer 1

The correct option is D $\frac{17}{4}$

Area $=\left|\underset{-2}{\overset{0}{\int }}ydx\right|+\left|\underset{0}{\overset{1}{\int }}ydx\right|$

$=\left|\underset{-2}{\overset{0}{\int }}{x}^3\right|+\left|\underset{0}{\overset{1}{\int }}{x}^{3}dx\right|$

$=\left|{\left(\frac{x^4}{4}\right)}_{-2}^0\right|+{\left(\frac{x^4}{4}\right)}_0^1$

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

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

$\frac{17}{4}$ sq. unit