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

F(x, y) = 2y + x; R is the rectangle defined by and .

D) 26

Question

Evaluate the double integral ​  ​
For the given function f(x, y) and the region R.
​
F(x, y) = 2y + x; R is the rectangle defined by  and  .
​
D) 26

Quizplus · Accepted Answer

To evaluate the double integral, we need to integrate the function f(x,y) over the given rectangular region R. So we have:

∬R f(x,y) dA = ∫[0,3] ∫[1,2] (2y+x) dydx

Evaluating the inner integral first, we get:

∫[1,2] (2y+x) dy = 2y^2/2 + xy |[1,2] = (2+2x)- (1+x) = x+1

Substituting this in the outer integral, we get:

∫[0,3] (x+1) dx = x^2/2 + x |[0,3] = 9/2+3 = 15/2 = 7.5

Therefore, the value of the double integral is 7.5, which is given by option B.

Evaluate the Double Integral ​ ​