Approximating Areas with Riemann Sums

Approximating Areas with Riemann Sums

12th Grade

15 Qs

quiz-placeholder

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Approximating Areas with Riemann Sums

Approximating Areas with Riemann Sums

Assessment

Quiz

Mathematics

12th Grade

Hard

Created by

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

Media Image

What does this picture represent?

Left Riemann Sum

Right Riemann Sum

Middle Riemann Sum

Trapezoidal Sum

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

What does picture represent?

Left Riemann Sum

Right Riemann Sum

Middle Riemann Sum

Trapezoidal Sum

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

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

Media Image

Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.

14

7

26

11

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