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

A) -10
B) 10e
C) 9
D) -9e

Question

Evaluate the double integral ​  ​
For the given function f(x, y) and the region R.
​  ; R is the rectangle defined by  and  .
​
A) -10 
B) 10e 
C) 9 
D) -9e

Quizplus · Accepted Answer

We need to evaluate the double integral of the function f(x, y) over the rectangular region R.

∫∫R f(x, y) dA

= ∫∫R x(y - 1) e^(xy) dA

= ∫2 to 3 ∫-2 to 2 x(y - 1) e^(xy) dx dy

= ∫2 to 3 [(e^(2y) - e^(-2y))/y] dy

= [(e^6 - e^(-6))/3] - [(e^4 - e^(-4))/2]

= 9

Therefore, the best choice is C) 9.

Evaluate the Double Integral ​ ​

Evaluate the Double Integral