1.
For this question, I was wondering if dividing the x through all of the terms would be the best way to start solving, which gives:
and then taking the antiderivative, evaluating from 1 to e etc...
2.
Also need help starting out this one. For this question does the derivative of need to first be taken? I do not know if it would be permissible to pull the d/dx out into the front of the integral, or even if that would help at all.
Additional thanks in advance.
For #2 - don't bother. Just evaluate F(b)-F(a) for your F(x). Good rule of thumb - if it looks ridiculous and crazy, there's no doubt some trick to make it not. I mean you'd have some seriously funky stuff going on here if they honestly expected you to take the integral of that function.
Thanks for the help,
I was ill during the lectures that introduced integration, I'm having a lot of difficulties catching up.
Just to clarify the theory behind this, for a continuous function:
is that what is happening in that question?
And if either the upper or the lower integration limits involved something in terms of 'x' how would that change the solution?
I have made a technical error here that has put you on the wrong track. The correct way of doing the question is to make the substitution . You therefore get where the integral terminals are left for you to find.
This is wrong since the derivative of a definite integral with respect to the variable of integration is zero (because you're differentiating a constant). I apologise for putting you on the wrong track.