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In multivariable calculus, what is a multiple integral used to calculate?
In multivariable calculus, what is a multiple integral used to calculate?
A multiple integral is used to calculate the definite integral of a function of several real variables.
What is the interpretation of multiple integrals in physics or natural philosophy?
What is the interpretation of multiple integrals in physics or natural philosophy?
In physics or natural philosophy, multiple integrals can be interpreted as representing surfaces, volumes, and other variables such as time and position.
What are integrals of a function of two variables over a region in $R^2$ called?
What are integrals of a function of two variables over a region in $R^2$ called?
Integrals of a function of two variables over a region in $R^2$ are called double integrals.
What are integrals of a function of three variables over a region in $R^3$ called?
What are integrals of a function of three variables over a region in $R^3$ called?
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What does the double integral of a positive function of two variables represent?
What does the double integral of a positive function of two variables represent?
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In multivariable calculus, a double integral of a positive function of two variables represents the ______ of the region between the surface defined by the function.
In multivariable calculus, a double integral of a positive function of two variables represents the ______ of the region between the surface defined by the function.
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Integrals of a function of three variables over a region in $R^3$ are called ______.
Integrals of a function of three variables over a region in $R^3$ are called ______.
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Integrals of a function of two variables over a region in $R^2$ are called ______.
Integrals of a function of two variables over a region in $R^2$ are called ______.
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For multiple integrals of a single-variable function, see the ______ formula for repeated integration.
For multiple integrals of a single-variable function, see the ______ formula for repeated integration.
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In physics or natural philosophy, the interpretation of multiple integrals includes variable to ______, position, etc. as well as surface, volume, etc. Inkl.
In physics or natural philosophy, the interpretation of multiple integrals includes variable to ______, position, etc. as well as surface, volume, etc. Inkl.
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