Chapter 5.1, Problem 11E

In the following exercises, estimate the volume of the solid under the surface z= f(x. y) and above the rectangular

legion R by using a Riemann sum with m = n = 2 and the sample points to be the lower left corners of the subrectangles of the partition.

11. The solid lying under the surface $z=\sqrt{4-y^2}$ and above the rectangular region R = [0. 2] $\times$ [0, 2] is illustrated in the following graph. Evaluate the double integral ${\displaystyle \underset{R}{\iint }f\left(x,y\right)dA}$. where $f\left(x,y\right)=\sqrt{4-y^2}$ . by finding the volume of the corresponding solid.