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Noble Knight
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Homework Statement
Evaluate double integral (x-y)^2 (sin (x+y))^2 dxdy taken over a square with successive vertices (pi,0), (2pi,pi), (pi,2pi), (0,pi)
Thank you.
Double Integral of (x-y)^2 (sin(x+y))^2 over a Square
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In summary, a multiple integral is an extension of a single integral to functions of multiple variables. It involves finding the integral of a function over a region in a multi-dimensional space. The main difference between a double integral and a triple integral is the number of variables and dimensions involved. Multiple integrals are typically evaluated using different integration techniques, depending on the type of integral and region of integration. They have significant applications in science and engineering, such as calculating volumes and masses, determining centers of mass, and solving problems in fluid mechanics and electromagnetism. There are also many real-life examples of multiple integrals, including calculating areas, determining fluid flow, and finding average temperatures.
Evaluate double integral (x-y)^2 (sin (x+y))^2 dxdy taken over a square with successive vertices (pi,0), (2pi,pi), (pi,2pi), (0,pi)
Thank you.
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tiny-tim
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Welcome to PF!
Hail, Noble Knight! Welcome to PF!
(have a pi: π and an integral: ∫ and try using the X2 icon just above the Reply box)
Prithee show us what thou hast tried, and where thou art perplexed, so that we may know how to aid thee!
Hail, Noble Knight! Welcome to PF!
(have a pi: π and an integral: ∫ and try using the X2 icon just above the Reply box
)Prithee show us what thou hast tried, and where thou art perplexed, so that we may know how to aid thee!
Last edited:
Related to Double Integral of (x-y)^2 (sin(x+y))^2 over a Square
1. What is a multiple integral?
A multiple integral is an extension of the concept of a single integral to functions of multiple variables. It involves finding the integral of a function over a region in a multi-dimensional space.
2. What is the difference between a double integral and a triple integral?
A double integral is an integral of a function of two variables over a two-dimensional region, while a triple integral is an integral of a function of three variables over a three-dimensional region. The main difference is the number of variables and dimensions involved.
3. How is a multiple integral evaluated?
A multiple integral is typically evaluated using the appropriate integration techniques such as Fubini's theorem, iterated integration, or change of variables. The specific method used depends on the type of integral and the region of integration.
4. What is the significance of multiple integrals in science and engineering?
Multiple integrals are used in a variety of scientific and engineering applications, such as calculating the volume and mass of irregularly shaped objects, determining the center of mass of a system, and solving problems in fluid mechanics and electromagnetism.
5. Are there any real-life examples of multiple integrals?
Yes, multiple integrals are used in many real-life scenarios, such as calculating the area under a curved surface in calculus, determining the flow of fluid through a pipe in engineering, and finding the average temperature of a room in thermodynamics.
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