How to calculate this integral?

  • Thread starter athrun200
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    Integral
In summary, We have a question about substitution and writing the range properly for calculating an electric field at a fixed point. The upper limit for the integral is θ = arctan(L) and the lower limit is 0, based on the given triangle.
  • #1
athrun200
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Homework Statement


attachment.php?attachmentid=37435&stc=1&d=1311346104.jpg



Homework Equations





The Attempt at a Solution


Can I use this substitution?
attachment.php?attachmentid=37436&stc=1&d=1311346104.jpg
 

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  • #2
Looks good, what does it come out to?
 
  • #3
hunt_mat said:
Looks good, what does it come out to?

attachment.php?attachmentid=37439&stc=1&d=1311346670.jpg


I am not sure for 2 things.

1. Since z is not a constant, does the derivative yield dz?
2. How can I write the range properly?
 

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  • #4
You're fixing a point z and calculating the electric field there, the limits are easy, you have [itex]L=\tan\theta[/itex] and so the upper limit is [itex]\theta =\tan^{-1}L[/itex], the lower on is just 0.
 
Last edited:
  • #5
hunt_mat said:
You're fixing a point z and calculating the electric field there, the limits are easy, you have [itex]L=\tan\theta[/itex] and so the upper limit is [itex]\theta \tan^{-1}L[/itex], the lower on is just 0.

Thx!
 
  • #6
For your limits of integration look at your triangle. (The angle you labeled L is actually θ.) If x = 0, then sin θ = 0 and if x = L, then sin θ = L/√(L2+z2) .
 

1. What is an integral?

An integral is a mathematical concept used to find the area under a curve. It is a fundamental tool in calculus and is often used to solve problems involving rates of change and accumulation.

2. How do I calculate an integral?

To calculate an integral, you need to use a specific method called integration. This involves finding the antiderivative of the function and then evaluating it at the upper and lower limits of integration.

3. What are the different types of integrals?

There are two main types of integrals: definite and indefinite. A definite integral has specific limits of integration and gives a numerical value, while an indefinite integral does not have limits and gives a general function.

4. Can integrals be solved without using formulas?

Yes, there are some integrals that can be solved without using formulas. These can be solved through techniques such as substitution, integration by parts, or trigonometric identities.

5. What are some common applications of integrals?

Integrals have many applications in fields such as physics, engineering, and economics. They are used to solve problems involving rates of change, motion, optimization, and area/volume calculations.

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