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For the longest time I would do integral problems in Calculus. I figured I understood how to do them because after I finished working problems, I would look in the back of my book and see my answers match what's there.

However, going into Physics, I see I really don't understand the whole IDEA behind integrals. When I say this, I mean that I'm never sure how to setup my integral for problems or even WHEN to use an integral.

For example, in one of my E. Science books, they posed this example question:

Derive the expression for the charge accumulated at the upper terminal of the element for t>0

and at this point the book had given me 2 ratios in differential form:

v = dw/dq

and

i = dq/dt

When the book told me to "derive the expression", this confused me because I can't with faith know exactly what to differentiate with respect to; that is, I'd just be guessing at things to differentiate with respect to until something lines up with what the book says.

Is something like this example problem a thing that only makes sense if you work out as many problems as possible or is it something that I can read around to get a better understanding of?

I do many problems in my 1st time physics class and I notice many times I don't know the direction to take with a problem unless I've seen it done before. So, is it something sort of like that to understand applications of integrals in physics?