How Do You Estimate a Double Integral Using Riemann Sums?

[AATroop]

Homework Statement

If R = [0,4]x[-1,2], use a Riemann sum with m=2, n=3 to estimate the value of ∫∫(1-xy^2)dA. Take the sample points to be the lower right corners.

Homework Equations

None

The Attempt at a Solution

2*1[f(2,-1) + f(2,0) + f(2,1) + f(4,-1) + f(4,0) + f(4,1)] = some value

Just wondering if the setup is correct, particularly the 2 and the 1 at the beginning.

Edit:

Would the solution for the upper left corners of the rectangles be

2*1[f(0,-1)+ f(0,0)+ f(0,1) +f(2,-1) + f(2,0) + f(2,1)]

 

[LCKurtz]

Homework Statement

If R = [0,4]x[-1,2], use a Riemann sum with m=2, n=3 to estimate the value of ∫∫(1-xy^2)dA. Take the sample points to be the lower right corners.

Homework Equations

None

The Attempt at a Solution

2*1[f(2,-1) + f(2,0) + f(2,1) + f(4,-1) + f(4,0) + f(4,1)] = some value

Just wondering if the setup is correct, particularly the 2 and the 1 at the beginning.

Yes, that looks OK

Edit:

Would the solution for the upper left corners of the rectangles be

2*1[f(0,-1)+ f(0,0)+ f(0,1) +f(2,-1) + f(2,0) + f(2,1)]

(0,-1) isn't the upper left corner of any rectangle. Did you accidentally do lower left?

 

[AATroop]

Yes, I think I did do lower left. I changed it and it came out to -8. Sounds close enough to me haha. Thanks a bunch for your help.