Evaluating Riemann Sum f(x,y) - 4x^2+y

[Derill03]

The problem says:

evaluate 4x^2+y by breaking into four congruent subrectangles and evaluating at the midpoints, 1=<x<=5 0=<y<=2

When i setup the rectangles these are my coordinates:

(1,1/2),(1,3/2),(3,1/2),(3,3/2) and delta A = 2

My answer comes out to be 168

When i integrate the function i get 338.6

The question then asks to compute the (riemann answer - the integral) which will be negative so I am not sure if i did the riemann correctly can someone check my work and give some feedback

 

[HallsofIvy]

The problem says:

evaluate 4x^2+y by breaking into four congruent subrectangles and evaluating at the midpoints, 1=<x<=5 0=<y<=2

When i setup the rectangles these are my coordinates:

(1,1/2),(1,3/2),(3,1/2),(3,3/2) and delta A = 2

This is wrong. The midpoints of the four subrectangles are at (2, 1/2), (2, 3/2), (4,1/2), and (4, 3/2). x ranges from 1 to 5, not 0 to 4. Or were you taking the left edge rather than the midpoint?

My answer comes out to be 168

When i integrate the function i get 338.6

The question then asks to compute the (riemann answer - the integral) which will be negative so I am not sure if i did the riemann correctly can someone check my work and give some feedback

There is no reason why that difference cannot be negative.