Use a midpoint sum with 5 sub-intervals to estimate the area between f(x) = x2 and the x-axis on [0, 1].
Answer
If we split [0, 1] into 5 sub-intervals we get sub-intervals of length 0.2. We need to know the following values of f:
Now we add them all up and multiply by 0.2:
Use a midpoint sum with 10 sub-intervals to estimate the area between f(x) = x2 and the x-axis on [0, 1].
If we split [0, 1] into 10 sub-intervals we get sub-intervals of length 0.1. We need to know the following values of f:
We add them all up to get 3.325, and then multiply by 0.1 to get our estimate:
3.325(0.1) = 0.3325.
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