Question

Let $f\left(x\right)=min\{x+1,\sqrt{1-x}\}$ then area bounded by $y=f\left(x\right)$ and x-axis is:

• A. $\frac{7}{6}$
• B. $\frac{5}{6}$
• C. $\frac{1}{6}$
• D. $\frac{11}{6}$

Answer 1

The correct option is A $\frac{7}{6}$

Clearly from the figure area bounded
$=$ Area under line from $-1$ to $0+$ Area under parabola from $0$ to $1$
Area 1 $=\frac{1}{2}$
Area 2 $={\int }_0^1\sqrt{1-x}dx$ = 2/3
Total Area $=1/2+2/3=7/6$