# How to get this integral into standard form

In summary, the conversation discusses the process of integrating 1/sqrt(c2-dv2) from first principles in the context of special relativity and Lorentz transformations. The speaker is attempting to manipulate the integral to get it into the usual form of an integral f(v) dv, but is unsure how to do so.

Gold Member
If I have the definite integral of 1/sqrt(c2-dv2) (without a dv after it), with c a real positive constant larger than the upper limit of the integral, how can I get it into the usual form of an integral f(v) dv ?

What you have written makes no sense at all. Can you give the context? Where did you see
$$\int \frac{1}{\sqrt{c^2- dv^2}}$$

I was attempting to work out from first principles an integration (which, I know, can be done much more easily with another point of view, but I wanted to see what this more difficult path would lead to) from special relativity, adding up infinitesimal increments dv of increases in velocity (I omitted the constants in my question). That is, this is from a Lorentz transformation.

## 1. How do I determine the limits of integration for an integral?

The limits of integration for an integral can be determined by looking at the given function and identifying the values that the variable can take. These values will then become the lower and upper limits of integration.

## 2. Can I change the order of integration for a double or triple integral?

Yes, the order of integration can be changed for a double or triple integral as long as the limits of integration are adjusted accordingly to match the new order.

## 3. What is the purpose of converting an integral into standard form?

Converting an integral into standard form allows for easier evaluation and comparison with other integrals. It also helps to identify patterns and relationships among different integrals.

## 4. Are there any specific techniques for converting an integral into standard form?

Yes, there are various techniques such as substitution, integration by parts, and using special trigonometric identities that can be used to convert an integral into standard form.

## 5. Is it necessary to convert an integral into standard form before evaluating it?

No, it is not necessary to convert an integral into standard form before evaluating it. However, it can make the evaluation process easier and more efficient in some cases.