Question

The area bounded by the curve $y=x^3-6x^2+8x$ and the $x$-axis is

• A. $8$ sq. units
• B. $\frac{8}{3}$ sq. units
• C. $\frac{3}{8}$ sq. units
• D. $6$ sq. units

Answer 1

The correct option is A $8$ sq. units

$y=x^3-6x^2+8x$, $=x(x-2)(x-4)$
$=\stackrel{2}{\underset{0}{\int }}(x^3-6x^2+8x)dx-\stackrel{4}{\underset{2}{\int }}(x^3-6x^2+8x)dx$
$=[\frac{x^4}{4}{|}_0^2-\frac{6x^3}{3}{|}_0^2+\frac{8x^2}{2}{|}_0^2]-[\frac{x^4}{4}{|}_2^4-3x^3{|}_2^4+4x^2{|}_2^4]$
$=8squnits.$