Mathematics: (a) Use a Riemann sum with m = n = 2 to estimate the value of the sin(x + y) dA R where R = [0, π] × [0, π]. Take the sample points to be lower left corners. (Round your answer to three decimal places.)

(a) Use a Riemann sum with m = n = 2 to estimate the

2Dgames

21.01.2022

4.9361

Step-by-step explanation:

Rieman sum = ∫∫ sin(x+y) ΔA

ΔA = ΔxΔy

Δx = $\frac{π -0}{2}$ = $\frac{π}{2}$ = pi/2 = Δy

ΔA = pi/2 * pi/2 = $\frac{pi^{2} }{4}$

Evaluating at the four corners

f(0,0) + f(0, pi/2) + f(pi/2,0) + f(pi/2, pi/2) =

sin(0 +0) + sin(0 + pi/2) + sin(pi/2 + 0) + sin(pi/2 , pi/2) = 0 +1 + 1 + 0 = 2

∫∫ sin(x+y) ΔA = 2 * $\frac{pi^{2} }{4}$ = $\frac{pi^{2} }{2}$ = 4.9361

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emory238

17.01.2022

gosh darn this is quite hard but I believe its 15?

Step-by-step explanation:

I could be wrong idk

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