Evaluate the double integral for the given function f(x, y) and the region R.
A)9
B)4
C)72
D)63

Question

Evaluate the double integral  for the given function f(x, y) and the region R. 
A)9 
B)4 
C)72 
D)63

Quizplus · Accepted Answer

First, we need to find the limits of integration.

For x: 0 ≤ x ≤ 3
For y: x ≤ y ≤ 3

Then we can evaluate the integral:

∫[0,3]∫[x,3] 4y dA
= ∫[0,3] (4y(y-x)) dx
= ∫[0,3] (4y^2 - 4xy) dx
= [4/3 * y^3 - 2xy^2] from y=x to y=3
= [(4/3)*27 - 18x] - [(4/3)*x^3 - 2x^3] 
= 72/3 - 2x^3
= 72/3 - 2(3^3)
= 72/3 - 54
= 18

Therefore, the answer is C.

Evaluate the Double Integral for the Given Function F(x