Question

The area bounded by the curve $y=(x-4)(x-1)$ and the $X$-axis is:

• A. $\frac{6}{5}$ sq. units
• B. $\frac{9}{4}$ sq. units
• C. $\frac{9}{2}$ sq. units
• D. $\frac{5}{6}$ sq. units

Answer 1

Answer: (C)

$\frac{9}{2}$ sq. units

$y=(x-4)(x-1)$
$y=x^2-5x+4$
$\stackrel{4}{\underset{1}{\int }}ydx=\stackrel{4}{\underset{1}{\int }}|(x^2-5x+4)|dx$
$=|\frac{x^3}{3}{|}_1^4-\frac{5x^2}{2}{|}_1^4+4x{|}_1^4|$

$=|\frac{63}{3}-5/2\left(15\right)+12|$
$=|21-\frac{75}{2}+12|$
=$\frac{9}{2}$ sq units.