?In the following exercises, estimate the volume of the solid under the surface \(z\) =

Chapter 5, Problem 10

(choose chapter or problem)

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

The level curves \(f(x,\ y)=k\) of the function \(f\) are given in the following graph, where \(k\) is a constant.

a. Apply the midpoint rule with \(m\) = \(n\) = \(2\) to estimate the double integral \(\iint_{R} f(x, y) d A\), where \(R=[0.1,\ 0.5]\times[0.1,\ 0.5]\)

Text Transcription:

z = f(x, y)

R

m = n = 2

f(x,\ y)=k

f

k

\iint_{R} f(x, y) d A

R=[0.1,\ 0.5]\times[0.1,\ 0.5]