What is the primary purpose of using Riemann sums in numerical integration?
MAT S213 Reviewer 2

Quiz
•
Mathematics
•
12th Grade
•
Medium
CHRISTOPHER PLAZA
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20 questions
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1.
MULTIPLE CHOICE QUESTION
20 sec • 2 pts
To approximate the area under a curve
To find the exact value of an integral
To solve differential equations
To calculate the derivative of a function
2.
MULTIPLE CHOICE QUESTION
20 sec • 2 pts
Which of the following best describes the error estimation in numerical integration?
The sum of the absolute values of the derivatives of the function being integrated
The difference between the exact value of the integral and its numerical approximation
The maximum value of the function over the interval of integration
The number of subintervals used in the approximation method
3.
MULTIPLE CHOICE QUESTION
45 sec • 2 pts
3.5
3.0
2.5
2.75
4.
MULTIPLE CHOICE QUESTION
20 sec • 2 pts
When using Trapezoidal rule, the number of subintervals must be:
A prime number
An even integer
An odd integer
Any positive integer
5.
MULTIPLE CHOICE QUESTION
20 sec • 2 pts
Which of the following is true about Riemann sums?
They can approximate the area under a curve by summing the areas of rectangles.
They can only be used with continuous functions.
They provide an exact value for the area under a curve.
They are more accurate than the Trapezoidal Rule and Simpson's Rule for all functions.
6.
MULTIPLE CHOICE QUESTION
20 sec • 2 pts
For approximating definite integrals, the error in the Trapezoidal Rule generally decreases as:
The function becomes more quadratic
The function becomes more linear
The width of each subinterval increases
The number of subintervals increases
7.
MULTIPLE CHOICE QUESTION
20 sec • 2 pts
Which of the following statements is true regarding the use of numerical integration methods?
Numerical integration methods can only approximate integrals of polynomial functions.
Numerical integration methods are always less accurate than finding the exact integral.
Numerical integration methods are useful for approximating integrals when the antiderivative of the function is difficult or impossible to find.
Numerical integration methods are unnecessary when the antiderivative of the function can be easily found.
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