- #1

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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?

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- Thread starter Apteronotus
- Start date

- #1

- 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

- 2,762

- 412

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

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- 0

- #4

- 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

- 1,707

- 5

it's a way to weight the domain.

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