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Comments on What to do when there's lot of function of time? (For integration) Should I consider them as constant?

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What to do when there's lot of function of time? (For integration) Should I consider them as constant?

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Let I have a function which is looking like this

$$f=\int\frac{l \ \mathrm {dt}}{\dot{\theta}r\dot{r}}$$

Here $\dot{\theta}$, $r$, $\dot{r}$ and $l$ all of them are function of $t$. For differentiating respect to time I simply increase "dot". But what to do for integration? Should I consider them as constant?

What will happen if I forcefully say that $r$ isn't constant? $r$ is changing every single sec.

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It is not true that for differentiating you simply “increase dot”. Rather, you apply the differentiat... (1 comment)
It is not true that for differentiating you simply “increase dot”. Rather, you apply the differentiat...
celtschk‭ wrote over 3 years ago

It is not true that for differentiating you simply “increase dot”. Rather, you apply the differentiation rules. Having said that, while taking the derivative usually can be done quite mechanically, integration cannot be done that way (well, technically it can, but the algorithm is so complicated that even computer algebra systems often don't fully implement it). Indeed, many integrals cannot be solved analytically at all.