Riemann sums Quiz
10 questions · easy to harder · Calculus · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 5 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Estimate the area under y = x2 from x = 0 to x = 3 with 3 left rectangles- A) 4 square units
- B) 5 square units
- C) 1 square units
- D) 0 square units
2 Question 2
Estimate the area under y = 2x + 1 from x = 0 to x = 4 with 4 left rectanglesType the answer.
3 Question 3
Estimate the area under y = 8 − x2 from x = 0 to x = 2 with 2 left rectangles- A) −15 square units
- B) 1 square units
- C) 15 square units
- D) 8 square units
4 Question 4
Estimate the area under y = x2 from x = 0 to x = 2 with 4 left rectanglesType the answer.
5 Question 5
Estimate the area under y = x2 from x = 0 to x = 3 with 3 midpoint rectangles- A) 0.25 square units
- B) 1 square units
- C) 87.5 square units
- D) 8.75 square units
6 Question 6
Estimate the area under y = 9 − x2 from x = 0 to x = 3 with 3 left rectanglesType the answer.
7 Question 7
Estimate the area under y = x3 + 1 from x = 0 to x = 2 with 2 right rectangles- A) 1 square units
- B) 9 square units
- C) 2 square units
- D) 11 square units
8 Question 8
Estimate the area under y = x2 − 2x + 2 from x = 0 to x = 3 with 6 left rectanglesType the answer.
9 Question 9
Estimate the area under y = x2 + 2 from x = 1 to x = 3 with 4 midpoint rectangles- A) 126.25 square units
- B) 0.5 square units
- C) 3.5625 square units
- D) 12.625 square units
10 Question 10
Estimate the area under y = 2x2 from x = 0 to x = 2 with 4 left rectanglesType the answer.