1. Evaluate the double integral for the functionf(x,y) and the given regionR.
R is the rectangle defined by-2  x  3 and1   y  e4
2. Evaluate the double integral
for the function f(x, y) and theregion R.
f(x, y) =
; R is bounded by the lines
x = 1, y = 0, and y = x.
3. Find the average value of the functionf(x,y) over the plane regionR.
f(x, y) = xy; R isthe triangle bounded by y = x, y = 2 -x, and y = 0
4. Verify that y is a general solution of thedifferential equation and find a particular solution of thedifferential equation satisfying the initial condition.
y =
;Â Â
= −2xy2;  y(0) = 7
