Question

The area (in sq. units) of the region described by
$A=\text{{}(x,y)\in R^2|y\ge x^2-5x+4,x+y\ge 1,y\le 0\text{}}$ is:

• A. $\frac{19}{6}$
• B. $\frac{17}{6}$
• C. $\frac{7}{2}$
• D. $\frac{13}{6}$

Answer 1

The correct option is A $\frac{19}{6}$

Required area $=A_1+A_2$
$=\frac{1}{2}\times 2\times 2+\left|\underset{3}{\overset{4}{\int }}(x^2-5x+4)dx\right|$
$=2+{|\frac{x^3}{3}-\frac{5x^2}{2}+4x|}_3^4$
$=2+|\frac{64}{3}-40+16-9+\frac{45}{2}-12|$
$=2+|-\frac{7}{6}|=2+\frac{7}{6}=\frac{19}{6}$ sq. units