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NODARman
- 57
- 13
- Homework Statement
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- Relevant Equations
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Hi, just wondering does this mean the triple integral of "y" with respect to "x"?
$$
\int \frac{d^{3} x}{y^{3}} .
$$
$$
\int \frac{d^{3} x}{y^{3}} .
$$
any context? bounds ? Complete problem statement ?NODARman said:Homework Statement:: .
Relevant Equations:: .
Hi, just wondering does this mean the triple integral of "y" with respect to "x"?
$$
\int \frac{d^{3} x}{y^{3}} .
$$
BvU said:any context? bounds ? Complete problem statement ?
I found it in a textbook, it's very general "equation".haruspex said:Is y a function of position in three dimensions?
What you posted is an expression, not an equation. What is the rest of it?NODARman said:I found it in a textbook, it's very general "equation".
A triple integral with respect to x and y is a mathematical operation that calculates the volume of a three-dimensional shape over a given region in the x-y plane. It is used in many fields of science, such as physics, engineering, and economics.
A double integral with respect to x and y calculates the area of a two-dimensional shape over a given region in the x-y plane, while a triple integral with respect to x and y calculates the volume of a three-dimensional shape over a given region in the x-y plane.
To solve a triple integral with respect to x and y, you must first determine the limits of integration for each variable (x, y, and z) and then evaluate the integral using the appropriate integration techniques, such as the method of slices or the shell method.
Triple integrals with respect to x and y have many real-world applications, such as calculating the mass of an object with varying density, determining the center of mass of a three-dimensional object, and finding the volume of a solid with a curved base.
Some common mistakes when using triple integrals with respect to x and y include incorrect determination of the limits of integration, using the wrong integration technique, and forgetting to include all necessary variables in the integrand. It is important to carefully check all steps of the calculation to avoid these errors.