Evaluate the double integral for the given function f(x, y) and the region R. ; R is the rectangle defined by
A) 5
B) 0
C) 3
D) - 5

Question

Evaluate the double integral  for the given function f(x, y) and the region R.  ; R is the rectangle defined by 
A) 5 
B) 0 
C) 3 
D) - 5

Quizplus · Accepted Answer

We can rewrite the given double integral as:
∬(R) 2xy dA = ∫[0,2] ∫[1,2] 2xy dy dx 
= ∫[0,2] (x)(2x - 2) dx 
= 2 ∫[0,2] (x^2 - x) dx 
= 2[(1/3)x^3 - (1/2)x^2] from 0 to 2 
= 2[(8/3) - 2] 
= -8/3 
Thus, the double integral evaluates to a constant (-8/3) which makes the answer (B) 0.

Evaluate the Double Integral for the Given Function F(x