4. Real Analysis

Riemann Integration — Quiz

Test your understanding of riemann integration with 5 practice questions.

Practice Questions

Question 1

Which of the following statements is true regarding the integrability of functions with a finite number of discontinuities on a closed interval $\left[a, b\right]$?

Question 2

Consider the function $f(x) = \begin{cases} 1 & \text{if } x \in \mathbb{Q} \\ 0 & \text{if } x \notin \mathbb{Q} \end{cases}$ on the interval $\left[0, 1\right]$. Which of the following statements is true about its Riemann integrability?

Question 3

If $f(x)$ is a continuous function on $\left[a, b\right]$, and $F(x)$ is an antiderivative of $f(x)$, which of the following expressions represents the definite integral of $f(x)$ from $a$ to $b$?

Question 4

What is the value of the definite integral $\int_0^1 (x^2 + 3) dx$?

Question 5

If $f(x)$ is a Riemann integrable function on $\left[a, b\right]$ and $c \in \left[a, b\right]$, which of the following properties of definite integrals is always true?