- #1

Apteronotus

- 202

- 0

What is the intuition behind integrating a function with respect to another function?

ex.

[tex]

\int f(t)dg

[/tex]

where g is itself a function of t?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Apteronotus
- Start date

- #1

Apteronotus

- 202

- 0

What is the intuition behind integrating a function with respect to another function?

ex.

[tex]

\int f(t)dg

[/tex]

where g is itself a function of t?

- #2

marcusl

Science Advisor

Gold Member

- 2,797

- 454

Since g is a function of t, you can apply the chain rule to give

[tex] \int f(t)d[g(t)]=\int f(t)\frac{d[g(t)]}{dt}dt=\int f(t)\.{g}(t) dt[/tex]

So you are finding the area under another curve that equals the first function weighted by the slope of the second.

- #3

l'Hôpital

- 258

- 0

- #4

Apteronotus

- 202

- 0

l'Hopital, I suppose if g is not differentiable then the equation can still be solved using stochastic calculus (ie. Ito integrals).

But my question has more to do with trying to understand

- #5

ice109

- 1,714

- 5

it's a way to weight the domain.

Share:

- Last Post

- Replies
- 6

- Views
- 601

- Replies
- 16

- Views
- 528

- Last Post

- Replies
- 1

- Views
- 472

- Replies
- 3

- Views
- 646

- Last Post

- Replies
- 2

- Views
- 718

- Last Post

- Replies
- 28

- Views
- 1K

- Replies
- 5

- Views
- 915

- Last Post

- Replies
- 5

- Views
- 970

- Replies
- 12

- Views
- 1K

- Replies
- 1

- Views
- 988