- #1

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## Main Question or Discussion Point

Really, I should know the answer to this, but...

Suppose I'm trying to perform an integration with respect to [itex]t[/itex]:

[tex]

\int_0^T f(\phi(t)) dt

[/tex]

So my function [itex]f[/itex] is explicitly a function of [itex]\phi[/itex], and [itex]\phi[/itex] depends on time [itex]t[/itex]. But then suppose I end up being able to write the integral as

[tex]

\int_0^T g(\phi(t)) \frac{d \phi}{dt} dt.

[/itex]

Can I just cancel the [itex]dt[/itex] and perform an integral with respect to [itex]\phi[/itex]? If so, I need to change the limits of integration, right?

Suppose I'm trying to perform an integration with respect to [itex]t[/itex]:

[tex]

\int_0^T f(\phi(t)) dt

[/tex]

So my function [itex]f[/itex] is explicitly a function of [itex]\phi[/itex], and [itex]\phi[/itex] depends on time [itex]t[/itex]. But then suppose I end up being able to write the integral as

[tex]

\int_0^T g(\phi(t)) \frac{d \phi}{dt} dt.

[/itex]

Can I just cancel the [itex]dt[/itex] and perform an integral with respect to [itex]\phi[/itex]? If so, I need to change the limits of integration, right?