Question

The area (in sq. units) of the region $\text{{}(x,y):0\le y\le x^2+1,0\le y\le x+1,\frac{1}{2}\le x\le 2\text{}}$ is:

• A. $\frac{23}{16}$
• B. $\frac{79}{24}$
• C. $\frac{79}{16}$
• D. $\frac{23}{6}$

Answer 1

The correct option is B $\frac{79}{24}$

Required Area $=\underset{\frac{1}{2}}{\overset{1}{\int }}(x^2+1)dx+\underset{1}{\overset{2}{\int }}(x+1)dx$
$={[\frac{x^3}{3}+x]}_{\frac{1}{2}}^1+{[\frac{x^2}{2}+x]}_1^2$
$=[\frac{4}{3}-\frac{13}{24}]+\frac{5}{2}=\frac{79}{24}$