Question

The area bounded by the curve $y=x^3-3x^2+2x$ and the $X$ - axis is (in square units )

• A. $\frac{1}{2}$
• B. $\frac{5}{2}$
• C. 1
• D. 4

Answer 1

Answer: (A)

Area Bounded by
$y=x^3-3x^2+2x$ and X -axis
$y=x\left(x^2-3x+2\right)$
$\Rightarrow y=x(x-1)(x-2)$
So, graph will be

Similarly part in 0 to 1 and 1 to 2
So, area $=2\underset{0}{\overset{1}{\int }}ydx$
$\Rightarrow 2\underset{0}{\overset{1}{\int }}{x}^3-3x^2+2xdx$
$\Rightarrow 2{\left[\frac{x^4}{4}-\frac{3x^3}{3}+\frac{2x^2}{2}\right]}_0^1$
$\Rightarrow 2\left[\frac{1}{4}-1+1-0\right]$
$=\frac{1}{2}$