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## Main Question or Discussion Point

For our homework this week for Pure, one of the questions is to ingration 1/(16 + x^2) with respect to x between the limits 0 and 4. I know the result from the formula wqith arctan in it, but since we've to use substitituion here and not just plonk down the formula, I'm confused as to what to substitute. Do I need to rearrange this eqt to work it out? I've got in my Applied notes how to differentiate the arctan thing to get this, but it doesn't make sense as to what I've to substitue in because at least when you differentiate you can work with eqt better. Even a hint to set me on the right track would be much-appreciated as I've got the other substituion questions okay but this one is bugging me as there seems to be more to it than the others.

Just one other thin about line integrals that we covered today. They make sense until I see what you've to put into the limits. For example

I= integral from A to B of xydx + integral from A to B of y^2dy

where A=(0,0) and B=(1,2)

The first case is where x=t and y=2t^2 and in brackets beside it has 0<=t<=2

I'vwe done the question and used he limits as 0 and 2, but only because it says beside the question. not because I know why! I mean whyy are the points given then? Do you work the limits out for t from the x=t and y=2t^2 eqts?

Just one other thin about line integrals that we covered today. They make sense until I see what you've to put into the limits. For example

I= integral from A to B of xydx + integral from A to B of y^2dy

where A=(0,0) and B=(1,2)

The first case is where x=t and y=2t^2 and in brackets beside it has 0<=t<=2

I'vwe done the question and used he limits as 0 and 2, but only because it says beside the question. not because I know why! I mean whyy are the points given then? Do you work the limits out for t from the x=t and y=2t^2 eqts?