Question

The area bounded by the curve $y=7x-10-x^2$ with $x$-axis is

• A. $9$ sq. units
• B. $3$ sq. units
• C. $9/2$ sq. units
• D. $4$ sq. units

Answer 1

The correct option is C $9/2$ sq. units

$y=7x-10-x^2$ $X$-axis
$=-(x^2-7x+10)$
$\stackrel{5}{\underset{2}{\int }}|(7x-10-x^2)|dx$
$=|\frac{7x^2}{2}-10x-\frac{x^3}{3}{|}_2^5|$
$|7/2(5^2-2^2)-10(5-2)-\left(\frac{5^3-2^3}{3}\right)|$
$|7/2\left(21\right)-10\left(3\right)-39|$
$|7/2\left(21\right)-69|$
$=9/2$ sq units.