Calc. 2 question?
I'm struggling with a Calculus 2 question regarding Riemann sums. Using the graph provided, could you help me find the values of L2, R2, and M2? I calculated L2 as 2(f(0) + f(2)), R2 as 2(f(2) + f(4)), and for M2, I took the average of the two heights. However, I keep getting flagged for my answers: L2 = 16, R2 = 32, and M2 = 24. Can someone clarify what I've done wrong?
1 Answers
Nov 16, 2024
I’m not entirely sure because even with your description of what you did, I can’t seem to verify the results you got.
My guess is that you overlooked the scale of the y-axis. Each grid square is 1.5 units tall. f(0) = 1.5 , f(2) = 7.5
L₂ = 2(1.5 + 7.5) = 2(9) = 18
——
For R₂ , f(2) = 7.5 , f(4) = 10.5
R₂ = 2(7.5 + 10.5) = 2(18) = 36
—-
As for the M₂ sum, I don’t think the method of averaging is correct. It’s attractive because it is easily calculated, but I don’t think it’s the correct way. I think you are supposed to estimate the value of f at the midpoint of the intervals by looking at the graph.
I’d estimate f(1) = 5 and f(3) = 9.5 to get
M₂ = 2(5 + 9.5) = 2(14.5) = 29
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