Chapter 5.1, Problem 49E

In the following exercises, the function f is given in terms of double integrals.

a. Determine the explicit form of the function f.

b. Find the volume of the solid tinder the surface z = f(x. v) and above the region R.

C. Find the average value of the function f on R.

d. Use a computer algebra system (CAS) to plot z = f(x. y) and z = f_avein the same system of coordinates.

49. [T] $f\left(x,y\right)={\displaystyle \underset{0}{\overset{y}{\int }}{\displaystyle \underset{0}{\overset{x}{\int }}\left(xs+yt\right)}dsdt}$where

$\left(x,y\right)\in R=\left[0,1\right]\times \left[0,1\right]$