- #1
ehrenfest
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Homework Statement
What technique would you use to do the integral:
[tex]\int_0^1 \int_0^1 dy dz \frac{1}{(1+y^2+z^2)^{5/2}} [/tex]
?
Eeh, no.Rainbow Child said:Yes. But after the integration, he can change back to cartesian coordinates.![]()
ehrenfest said:Maybe there is no reasonable way to do it. Mathematica gave a nice simple answer so I thought there would be. But I was probably wrong.
coomast said:Can this result be confirmed by anyone?
arildno said:Not utterly trivial, Rainbow Child:
Although the "radial" integration will go easy enough, the limits for the unit square, as represented in polar coordinates are somewhat nasty.
Rainbow Child said:Then it's trivial.
An integral is a mathematical concept used to calculate the area under a curve or the accumulation of a quantity over a specific interval. It is the reverse process of differentiation, and it is used to solve a wide range of problems in mathematics and science.
Integrals are essential in many scientific and engineering fields, including physics, chemistry, economics, and more. They allow us to calculate important quantities such as displacement, velocity, acceleration, and work. Having a strong understanding of integrals is crucial for solving real-world problems and making accurate predictions.
There are several techniques for solving integrals, including substitution, integration by parts, partial fractions, trigonometric substitution, and more. Each technique is useful for different types of integrals and can be applied depending on the complexity of the problem.
The choice of technique depends on the form of the integral. Some integrals may be solved using more than one technique, while others may require a specific approach. It is essential to analyze the integral and try different techniques until a solution is found.
Yes, integrals can be solved using software or calculators, but it is still necessary to have a basic understanding of the different techniques to verify the accuracy of the solution. Additionally, some integrals may be too complex for software or calculators to solve, so having a strong grasp of the techniques is essential for tackling these problems.