Find the area bounded curve $y = (x - 1)^3$, $x-$axis and the ordinates $x = -1$ and $x = 2$.

Question

Find the area bounded curve $y = (x - 1)^3$, $x-$axis and the ordinates $x = -1$ and $x = 2$.

Shaded Area $= \int_{-1}^{1}(-y)\cdot dx + \int_{1}^{2}(y)\cdot dx$

$= -\int_{-1}^{1}(x-1)^3\cdot dx + \int_{1}^{2}(x-1)^3\cdot dx$

On integrating and putting limit $= 4 + \frac{1}{4}$
$=\frac{17}4$

I know how the curve will look like also how to find the area but I am getting a feeling that while evaluating I'm getting the wrong area. Can someone please guide?

Answer 1

It looks fine to me. Well done.