11. Riemann Integration I

Partitions And Upper/lower Sums — Quiz

Test your understanding of partitions and upper/lower sums with 5 practice questions.

Practice Questions

Question 1

Which of the following is a partition of the interval $[0,2]$?

Question 2

Let $f(x)=3$ on $[1,4]$. For any partition of $[1,4]$, what is the value of both the upper sum and the lower sum?

Question 3

For $f(x)=x$ on $[0,2]$ and the partition $\{0,1,2\}$, what is the lower sum?

Question 4

For $f(x)=x^2$ on $[0,1]$ and the partition $\{0,\tfrac{1}{2},1\}$, what is the upper sum?

Question 5

For any bounded function $f$ on $[a,b]$ and any partition $P$, which inequality is always true?