Answer:
4.9361
Step-by-step explanation:
Rieman sum = ∫∫[tex]sin(x+y)[/tex]ΔA
ΔA = ΔxΔy
Δx = [tex]\frac{π -0}{2}[/tex] = [tex]\frac{π}{2}[/tex] = pi/2 = Δy
ΔA = pi/2 * pi/2 = [tex]\frac{pi^{2} }{4}[/tex]
Evaluating at the four corners
[tex]f(0,0) + f(0, pi/2) + f(pi/2,0) + f(pi/2, pi/2)[/tex] =
[tex]sin(0 +0) + sin(0 + pi/2) + sin(pi/2 + 0) + sin(pi/2 , pi/2) = 0 +1 + 1 + 0[/tex] = 2
∫∫[tex]sin(x+y)[/tex]ΔA = 2 * [tex]\frac{pi^{2} }{4}[/tex] = [tex]\frac{pi^{2} }{2}[/tex] = 4.9361
