Riemann sums Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/calculus/riemann-sums/quiz/

1. 1

   Estimate the area under y = x² from x = 0 to x = 3 with 3 left rectangles
   1. A) 4 square units
   2. B) 5 square units
   3. C) 1 square units
   4. D) 0 square units

2. 2

   Estimate the area under y = 2x + 1 from x = 0 to x = 4 with 4 left rectangles

   Answer: ____________________

3. 3

   Estimate the area under y = 8 − x² from x = 0 to x = 2 with 2 left rectangles
   1. A) −15 square units
   2. B) 1 square units
   3. C) 15 square units
   4. D) 8 square units

4. 4

   Estimate the area under y = x² from x = 0 to x = 2 with 4 left rectangles

   Answer: ____________________

5. 5

   Estimate the area under y = x² from x = 0 to x = 3 with 3 midpoint rectangles
   1. A) 0.25 square units
   2. B) 1 square units
   3. C) 87.5 square units
   4. D) 8.75 square units

6. 6

   Estimate the area under y = 9 − x² from x = 0 to x = 3 with 3 left rectangles

   Answer: ____________________

7. 7

   Estimate the area under y = x³ + 1 from x = 0 to x = 2 with 2 right rectangles
   1. A) 1 square units
   2. B) 9 square units
   3. C) 2 square units
   4. D) 11 square units

8. 8

   Estimate the area under y = x² − 2x + 2 from x = 0 to x = 3 with 6 left rectangles

   Answer: ____________________

9. 9

   Estimate the area under y = x² + 2 from x = 1 to x = 3 with 4 midpoint rectangles
   1. A) 126.25 square units
   2. B) 0.5 square units
   3. C) 3.5625 square units
   4. D) 12.625 square units

10. 10

    Estimate the area under y = 2x² from x = 0 to x = 2 with 4 left rectangles

    Answer: ____________________