Solving Bizarre Integral: x/[z2(x2+z2)1/2]

  • Thread starter Bigfoots mum
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In summary, the purpose of solving this bizarre integral is to find the definite integral of a function that includes both x and z variables. The first step in solving this integral is to simplify the expression by factoring out common terms and then using trigonometric substitutions or other integration techniques. This integral can be solved analytically by using integration techniques such as trigonometric substitutions, u-substitution, or integration by parts. However, if the integral is too complex, numerical methods such as Simpson's rule or the trapezoidal rule can be used to approximate the solution. One limitation of solving this integral is that the function must be continuous and defined for all values of x and z. Special cases may arise if the function is undefined or
  • #1
Bigfoots mum
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Now then, I am close to shedding a tear with this one.

This integral has been popping up in a few electromag examples iv been doing and i have absolutely no idea what's going on here.

The integral is 1/[(x2+z2)3/2] with respect to x

According to the textbook the answer is x/[z2(x2+z2)1/2]

I initially, without evening really thinking, went straight for -1/(x[x2+z2]1/2)

Any ideas?
Thanks
 
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  • #2
Use the substitution [itex]x=z \tan u[/itex].
 
  • #3
btw, you left a constant
 

1. What is the purpose of solving this bizarre integral?

The purpose of solving this bizarre integral is to find the definite integral of a function that includes both x and z variables.

2. How do you approach solving this integral?

The first step in solving this integral is to simplify the expression by factoring out common terms and then using trigonometric substitutions or other integration techniques.

3. Can this integral be solved analytically or does it require numerical methods?

This integral can be solved analytically by using integration techniques such as trigonometric substitutions, u-substitution, or integration by parts. However, if the integral is too complex, numerical methods such as Simpson's rule or the trapezoidal rule can be used to approximate the solution.

4. Are there any special cases or limitations when solving this integral?

One limitation of solving this integral is that the function must be continuous and defined for all values of x and z. Special cases may arise if the function is undefined or discontinuous for certain values of x and z.

5. What are some real-world applications of solving this integral?

Solving this integral can be useful in various fields such as physics, engineering, and economics. It can be used to calculate the displacement, velocity, or acceleration of a moving object, determine the work done by a force, or find the area under a curve in economic models.

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