Question

Area of region $\{(x,y)\in R^2:y\ge \sqrt{|x+3|},5y\le x+9\le 15\}$ is equal to

• A. $\frac{1}{6}$
• B. $\frac{4}{3}$
• C. $\frac{3}{2}$
• D. $\frac{5}{3}$

Answer 1

Answer: (C)

$\frac{3}{2}$

Area $ABE$ (under parabola) $={\int }_{-4}^{-3}\sqrt{-x-3}dx=\frac{2}{3}$

Area $BCD$ (under parabola) $={\int }_{-3}^1\sqrt{x+3}dx=\frac{16}{3}$
Area of trapezium $ACDE$ $=\frac{1}{2}(1+2)5=\frac{15}{2}$
Required area $=\frac{15}{2}-\frac{16}{3}-\frac{2}{3}=\frac{3}{2}$