Approximate the double integral. , where R is bounded by x = 0, x = 3, y = 0, and y = x + 2
A) 2.636
B) 2.658
C) 0.886
D) 1.772

Question

Approximate the double integral.  , where R is bounded by x = 0, x = 3, y = 0, and y = x + 2
A) 2.636 
B) 2.658 
C) 0.886 
D) 1.772

Quizplus · Accepted Answer

We can set up the integral as follows:

$\int_0^3 \int_0^{x+2} 11e^{x+y} dy dx$

Then we can evaluate the integral:

$\int_0^3 \int_0^{x+2} 11e^{x+y} dy dx = 11\int_0^3 e^x \int_0^{x+2} e^y dy dx = 11\int_0^3 e^x (e^{x+2} - e^x) dx$

$= 11\int_0^3 e^{3x+2} - e^{2x} dx = \frac{11}{3}(e^8 - e^2) \approx 2.658$

Therefore, the best choice is B.

Approximate the Double Integral