Question

Problem 3. Let $f(x) = \begin{cases} 1, & \text{if } x = \frac{1}{k} \text{ for some } k \in \mathbb{N}, \\ 0, & \text{otherwise.} \end{cases}$. Prove that $f$ is Riemann integrable on $[0, 1]$ and calculate $\int_0^1 f(x)dx.$

          Problem 3. Let $f(x) = \begin{cases} 1, & \text{if } x = \frac{1}{k} \text{ for some } k \in \mathbb{N}, \\ 0, & \text{otherwise.} \end{cases}$. Prove that $f$ is Riemann integrable on $[0, 1]$ and calculate $\int_0^1 f(x)dx.$

Problem 3. Let f(x) = 1, if x = (1)/(k) for some k ∈ℕ,
0, otherwise.. Prove that f is Riemann integrable on [0, 1] and calculate ∫0^1 f(x)dx.

Added by Patricia S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

05/19/2022

Step 1

Step 1: To prove that f(x) = x is Riemann integrable on [0,1], we need to show that the upper and lower Riemann sums converge to the same value as the partition of the interval [0,1] becomes finer. Show more…

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