Calc. 2 question?

Use the graph to find L2, R2 and M2.

Is L2= 16, R2=32, and M2= 24 not right?!

It keeps saying it is wrong and I have no idea what I did wrong.

For L2, I did 2(f(0)+f(2))

For R2, I did 2(f(2)+f(4))

And for the midpoint I did the average of the two.

What am I doing wrong?

1 Answer

  • 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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