What is Fubini's theorem?
Fubini’s theorem. Finding the limits of integration.

Quiz
•
Mathematics
•
12th Grade
•
Medium
Arina Ussubaliyeva
Used 4+ times
FREE Resource
12 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Mean value theorem
Dirichlet's principle
Result from mathematical analysis
Law of Large Numbers
Answer explanation
Fubini's theorem is a result from mathematical analysis.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What conditions are necessary to apply Fubini's theorem?
The function to be integrated must be derivative with respect to each of the variables
The integrable function must be integrable with respect to each of the variables separately.
The function being integrated must be unlimited
The function being integrated must be linear
Answer explanation
To apply Fubini's theorem, the integrable function must be integrable with respect to each variable separately.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the limits of integration?
Difference of function values
Sum of all function values
The interval over which the function is integrated
Derivative of a function
Answer explanation
The limits of integration refer to the interval over which the function is integrated. It determines the range of values for which the function is evaluated.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How to find the limits of integration for a double integral?
Study the region of integration and determine the boundaries of this region for each variable
Ignore region of integration
Use the Newton-Leibniz formula
Randomly select any limits
Answer explanation
To find the limits of integration for a double integral, study the region of integration and determine the boundaries for each variable.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What steps do you need to follow to apply Fubini's theorem?
Perform triple integral
Perform a double integral over the area, breaking it into two one-dimensional integrals
Apply Gauss' formula
Use Euler's method
Answer explanation
To apply Fubini's theorem, perform a double integral over the area, breaking it into two one-dimensional integrals. This allows for easier calculation and understanding of the problem.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What problems may arise when finding the limits of integration?
Determining the exact limits and selecting appropriate limits
Losing limits
Changing the color of the limits
Wrong spelling of limits
Answer explanation
The main problems when finding limits of integration are determining the exact limits and selecting appropriate limits.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What methods can be used to simplify finding the limits of integration?
Change of variable, symmetry of function, known integrals
Multiplying a variable by a constant, dividing a variable by a constant, adding a variable to a constant
Using trigonometric functions, finding the derivative of a function, using L'Hopital's rule
Using Euler's method, finding the inverse function, using Simpson's rule
Answer explanation
To simplify finding limits of integration, you can use methods such as change of variable, symmetry of function, and known integrals. These methods help in determining the correct limits.
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