Question

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

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

Answer 1

Answer: (B)

Required area = $A_1+A_2$
$=\frac{1}{2}\times 2\times 2+\left|{\int }_3^4\left(x^2-5x+4\right)dx\right|$
$=2+\frac{7}{6}=\frac{19}{6}$sq units