Let f(x) = {1, if 0 < x ≤ 1 and 0, if x = 0}?
Let f(x) = {1, if 0 < x ≤ 1 and 0, if x = 0}
Show that f is Riemann integrable on [0, 1].
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Let f(x) = {1, if 0 < x ≤ 1 and 0, if x = 0}
Show that f is Riemann integrable on [0, 1].
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Let a be a positive number less than 1 and consider Integral(a,1){f(x)dx} =
Integral(a,1){1dx} = x (from a to 1) = 1 - a. Now take the limit as a -> 0, and the limit is 1.