Question

For which of the following values of $m$, is the area of the region bounded by the curve $y=x-x^2$ and the line $y=mx$ equals 9/2 sq. unit

• A. -4
• B. -2
• C. 2
• D. 4

Answer 1

Answer: (B), (D)

The correct options are
B 4
D -2

$-x^2+x=mx$
$-x+1=m$
$x=1-m$
So, area $\stackrel{1-m}{\underset{0}{}\int }\left[\right(x-x^2)-mx]dx$
$\stackrel{1-m}{\underset{0}{}\int }\left[\right(1-m)x-x^2]dx=9/2$
$=\frac{(1-m)x^2}{2}-\frac{x^3}{3}=9/2\Rightarrow$ $\frac{|(1-m){|}^3}{6}=9/2$
$=\frac{|(1-m){|}^3}{3}=9$
$\left|\right(1-m\left)\right|=3$
$\Rightarrow 1-m=\pm 3$
$m=4;m=-2$