I am studying a paper and a math step like this was used:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

dt'=(1+\frac{h}{2}sin^2(\theta))dr \\

\int^{t1}_t dt'=\int^d_0 (1+\frac{h}{2}sin^2(\theta))dr \\

where\\

h=h(t-\frac{r}{c}-\frac{r}{c}cos(\theta))

[/tex]

This seems wrong because it seems to me that you're not doing the same thing to both sides of the equation. You ought to integrate both sides with respect to t', correct? Is there some change of variables I'm not seeing here? Or in infinitesimal equations like that, can you really just integrate each term with respect to the differential factor's corresponding variable?

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# I Integrating both sides of an equation question

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