• Support PF! Buy your school textbooks, materials and every day products Here!

Integration question involving square root

  • Thread starter binbagsss
  • Start date
  • #1
1,208
9
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.
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

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.
 
  • #3
220
91
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.
 
  • #4
1,208
9
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 ;)
 
  • #5
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,511
5,442
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.
 

Related Threads on Integration question involving square root

  • Last Post
Replies
13
Views
15K
Replies
3
Views
2K
Replies
4
Views
815
Replies
7
Views
2K
Replies
3
Views
1K
Replies
4
Views
2K
Replies
6
Views
10K
Replies
1
Views
4K
Replies
1
Views
2K
Replies
6
Views
1K
Top