The area bounded by the curve y = x3, the x-axis and the ordinates x = –2 and x = 1 is
Answer & explanation
Correct answer: option 4
The bounded area is shown shaded in the fig.
The required Area = Area(OABO) + Area(OCDO)
$=\begin{vmatrix}\int\limits_0^1x^3dx\end{vmatrix}+\begin{vmatrix}\int\limits_{-2}^0x^3dx\end{vmatrix}=\begin{vmatrix}\frac{x^4}{4}\end{vmatrix}_0^1+\begin{vmatrix}\frac{x^4}{4}\end{vmatrix}_{-2}^0$
$=\frac{1}{4}+4=\frac{17}{4}$ sq. units.
Hence (D) is the correct answer.