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Q.
The area bounded by the curve $y=x^{3}-3 x^{2}+2 x$ and the $X$ - axis is (in square units )
TS EAMCET 2018
Solution:
Area Bounded by
$y=x^{3}-3 x^{2}+2 x$ and X -axis
$y=x\left(x^{2}-3 x+2\right)$
$\Rightarrow \, y=x(x-1)(x-2)$
So, graph will be
Similarly part in 0 to 1 and 1 to 2
So, area $=2 \int\limits_{0}^{1} \,y d x $
$ \Rightarrow \,2 \int\limits_{0}^{1} x^{3}-3 x^{2}+2 x d x$
$\Rightarrow \, 2\left[\frac{x^{4}}{4}-\frac{3 x^{3}}{3}+\frac{2 x^{2}}{2}\right]_{0}^{1} $
$\Rightarrow \,2\left[\frac{1}{4}-1+1-0\right]$
$=\frac{1}{2}$
