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Riemann Sums Interval?
I am given the definite integral of Sqrt(x) with the interval [0,36] and 18 equally spaced sub-intervals.
What is the minimum number of equally spaced intervals needed in the case that the difference between the upper and lower Riemann sum estimates for the definite integral is less than 1.
1 Answer
- ?Lv 76 years ago
f(x) is an increasing function
the lower sum = left hand sum
the upper sum = right hand sum
the difference comes down to the endpoints.
L = ∑ [i = 0 to n-1 ] (36i/n)^1/2 (36/n)
U =∑ [i = 1 to n ] (36i/n)^1/2 (36/n)
U - L = (36)^1/2 (36/n)
216 / n < 1
n > 216
