Integration question involving square root

Click For Summary

Homework Help Overview

The discussion revolves around integrating two differential equations involving square roots: one with the expression \(\sqrt{\frac{k}{x}-1}\) and the other with \(\sqrt{\frac{k}{x}+1}\), where \(k\) is a constant. Participants express uncertainty regarding appropriate substitutions for integration.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss potential substitutions, with some suggesting trigonometric methods. There is a mention of expressing the integrals in a simpler form and considering integral tables. Concerns about deriving solutions from first principles are also noted.

Discussion Status

Some participants have offered guidance on starting points, such as writing the equations as integrals and exploring substitutions. There is an acknowledgment of the need for individual effort in problem-solving, but no consensus has been reached on a specific method.

Contextual Notes

Participants note a lack of clarity on the necessary substitutions and the challenge of deriving answers from first principles. There is an emphasis on the importance of trying various approaches.

binbagsss
Messages
1,291
Reaction score
12
Member warned that an effort must be shown

Homework Statement



How to integrate

## \frac{dx}{dt}=\sqrt{\frac{k}{x}-1}##

AND

## \frac{dx}{dt}=\sqrt{\frac{k}{x}+1}##

k a constant here.

I'm unsure what substitution to do.
Many thanks in advance.

Homework Equations

The Attempt at a Solution



I can't really get started as I'm unsure what substition is needed.
I think a trig but don't know what?many thanks in advance.
 
Physics news on Phys.org
binbagsss said:

Homework Statement



How to integrate

## \frac{dx}{dt}=\sqrt{\frac{k}{x}-1}##

AND

## \frac{dx}{dt}=\sqrt{\frac{k}{x}+1}##

k a constant here.

I'm unsure what substitution to do.
Many thanks in advance.

Homework Equations

The Attempt at a Solution



I can't really get started as I'm unsure what substition is needed.
I think a trig but don't know what?many thanks in advance.

You need to show more effort. Just try lots of different things. Some of them will be a wast of time, but others should work. Trying it on your own first is the only way to learn.
 
Try expressing your integrals in a form that can be found in a table of integrals. It took me two minutes to find the answer to your question. If you are supposed to derive your answer from first principles, at least you will have something to work towards.
 
Fred Wright said:
Try expressing your integrals in a form that can be found in a table of integrals. It took me two minutes to find the answer to your question. If you are supposed to derive your answer from first principles, at least you will have something to work towards.

I've been warned already. cheers for the input though my good pal ;)
 
binbagsss said:
I can't really get started
A good start would be to write as an integral, in as simple a form as you can, instead of leaving it as a differential equation.
Next, look for a substitution that gets k out of the way. Then think about a trig substitution.
 

Similar threads

  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
Replies
12
Views
2K
Replies
4
Views
3K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
4
Views
2K
  • · Replies 15 ·
Replies
15
Views
3K