Approximating Areas with Riemann Sums

Quiz
•
Mathematics
•
12th Grade
•
Hard
Anthony Clark
FREE Resource
15 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
3.75
4.5
5
7
Answer explanation
The Midpoint Rule with 2 subintervals gives an approximation of 4.5 for the area under the curve y = x^3 from x = 1 to x = 2.
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
8
10
12
14
Answer explanation
The Midpoint Rule with 2 subintervals gives an approximation of 10 for the integral of (2x + 1) from 1 to 3.
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
When calculating the numerical approximation of an integral using the Trapezoidal Rule, which of the following factors does not affect the accuracy of the approximation?
The smoothness of the function being integrated
The number of subintervals
The method used to calculate the function's values at the endpoints of the subintervals
The color of the graph of the function
Answer explanation
The color of the graph of the function does not affect the accuracy of the Trapezoidal Rule approximation.
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What does this picture represent?
Left Riemann Sum
Right Riemann Sum
Middle Riemann Sum
Trapezoidal Sum
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What does picture represent?
Left Riemann Sum
Right Riemann Sum
Middle Riemann Sum
Trapezoidal Sum
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)
5(3) + 1(4) + 2(5) + 1(7)
5(4) + 1(5) + 2(7) + 1(6)
5(3) + 6(4) + 8(5) + 9(7)
0(3) + 5(4) + 6(5) + 8(7)
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.
14
7
26
11
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