Evaluate the double integral for the function f(x,y) and the given region R. R is the rectangle defined by -

Evaluate the double integral for the function f(x,y) and the given region R.

R is the rectangle defined by -2 less than or equal to x less than or equal to 3 and 1 less than or equal to y less than or equal to e^3

Via iterated integration, ∫∫R (x/y) dA
= ∫(x = -2 to 3) ∫(y = 1 to e^3) (x/y) dy dx
= ∫(x = -2 to 3) x ln |y| {for y = 1 to e^3} dx
= ∫(x = -2 to 3) x * (3 - 0) dx
= (3/2)x^2 {for x = -2 to 3}
= 15/2.

I hope this helps!