Once again I am stumped by integration with substitution. I have two problems which are probably a breeze for some of you, but I just seem to be doing this ---> .
1. where the substitution is
and
2. where the substitution is
Thanks for any help
Once again I am stumped by integration with substitution. I have two problems which are probably a breeze for some of you, but I just seem to be doing this ---> .
1. where the substitution is
and
2. where the substitution is
Thanks for any help
First things first, remember to put in your "dx", when writing the integral. That thing is crucial to subsitution.
1. where the substitution is
and
2. where the substitution is
1.
Hence . Just replace xdx with that, and replace x^2+3 with u.
2.
You need to write in terms of so you can use your substitution, s.
[quote=Beard;241407]Once again I am stumped by integration with substitution. I have two problems which are probably a breeze for some of you, but I just seem to be doing this ---> .
If we make the sub . We make the subs and get:1. where the substitution is
Now, go to town.
Thanks but I had already done those processes with both of them, its just getting past that point that I find difficult.
i.e. the first one
and
then,as you were saying,
which would then mean
. Carrying on, if I was then to integrate this I would get
.
Is this correct?
then the second one I had done what you said before but I just get sort of tangled up.
where due to the trigonometric identity
becomes
or
also .
And *ding* the lightbulb goes on, for the second one anyway. As it finishes:
becoming
Although you said I was right for the first question, my books disagrees, and although I would love to believe the book is wrong it generally isn't and it gives the answer of:
All settled, here, I know, but here's a couple of pics...
As usual, straight continuous lines diff/anti-diff with respect to x, straight dashed lines with respect to the dashed balloon expression.
Don't integrate - balloontegrate! Balloon Calculus: worked examples from past papers