[LifeIsGood]

I got parts a & b but there's something I want to ask in general but using this as an example. In part c) I have to do dx/du but how do I know when to do that? I'm sure it hasn't come up in all the papers but I tripped up on the question because I got up to :

4/2 (b:a)[x^3(lnu)du] but didn't get past this stage till I went through it with Exam Solutions, can anyone tell me when to look out for it please

[notnek]

You have



and you need to change this to an integral du using the substitution

The way to change dx to du is to find du/dx:



Now substutute everything in, remembering that .

Post your working if you're still stuck. Or post the specific part that confuses you.

[james22]

You have to do dx/du (or similar) for every substitution. It is how you change the dx into a du.

[LifeIsGood]

Thank you both, I got it now

I was getting confused before because I thought it was an additional step. One question though - when you're finding the area/volume of a curve using Integration and I know when they are parametric, you add a little bit after the integral of y^2 as in it'll dx/dt*dt or something?