## Thomas' Calculus 13th Edition

2+$\frac{\pi}{2}$
y=1+$\sqrt{1-x^2}$ y-1=$\sqrt{1-x^2}$ (y-1)$^2$=1-x$^2$ $x^2$+(y-1)$^2$=1 is the upper Semicircle. the area of this semicircle is A=$\frac{1}{2}\pi r^2$ =$\frac{1}{2}\pi(1)^2$=$\frac{\pi}{2}$ The area of the rectangle base is A=$Lw$ =(2)(1)=2. Then the total area is 2+$\frac{\pi}{2}$ =>$\int_{-1}^1(1+\sqrt{1-x^2})dx$ =$2+\frac{\pi}{2}$ square units as shown in given diagram