Hello,
I have an exercise with solution and I don't understand it.
Calculate:
Solution:
Substitution:
will be substituted by and by
Up to here I understand it but now comes the problem.
The book says, that in the integral is still a . Okay. Now they solve the equation and get , so that the hole substitution leads to:
What are the mathematical reasons for the equation ?
I have no idea from where this come from.
They got it from but why is this allowed?
Thanks for help
Hi,
thats not my problem. I want to know why am I allowed to do this. They solve the function , thats easy but why?
Up to this step the integral is
I don't understand the reason, the mathematical rules what has to do with the other in the integral, because the substitution is only .
I said that I got this calculation to that point. I don't understand what has to do with the other x in the integral. Why can I calculate this eauation? Not how. The calculation is trivial but I didn't understand the relation between the function and the other .
I guess I didn't see the forrest because of the trees...
I don't understand what you are asking. Is your problem with differentiation, substitution, or what? Be specific. We have all been where you are, but in order for us to help you, you are going to have to be precise in what you are asking. Mathematics is all about presicion...
Thinking about composite functions is unnecessary for completing the task at hand.
When we integrate, our objective is to make the integrand easy to work with. Here's what I'm gonna do:
I'm gonna do this integral from scratch, and then ou tell me when you get lost.
1. Problem:
2. Notice that making the substitution might get me somewhere, because as it stands now, this particular integral is nasty. The key is to TRY SOMETHING. Anything at all.
3. If then by solving for x I obtain .
4. Differentiate which implies that
5. Look at the original problem and make the substitutions
giving us
So, where is your trouble. Step 1? 2? 3? etc...
I have only with one word a problem. In step three you say "obtain". If I obtain I got everything. "Obtain" is the problem.
The rule of substitution in general says:
Is continous differentiable and an intervall with and piecewise continous, than is
I understand the scentence and the proof of it but I can not apply it to the example above. The other is not an argument of , so why we can obtain this? We know nothing about the area of definition here.
Argh, I guess I am too stupid to see the answer
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Story dedicated to the general, you know who you are.
OK.
You have an integral in terms of "x".
and you did a U-Substitution.
then you should convert everything in the original integral in the corresponding value in terms of u according to your substitution.
VonNemo19 explained it two times, then he explained it as a steps.
and you have just moved on a circular.
I tried to explain it to you 5 times, But really I can not.
Do you know why?
Because it is clear !
do not ask yourself this kind of questions.
try to ask yourself -as an example- " What if it is , Can I integrate it ?
What If it was tan(x) there, Can I integrate it ?
These kind of questions will help you.
such questions will let you bring your pen and your papers and do a "GOOD TRY", they will learn you new methods for integrating things.
Did you see the difference between them ?
Your question makes you moving around a circular.
but the other questions let you learn new methods .
Come on, There is many people on our earth who can not just pass Calculus I !
Sure you are better than them.
always try to search about the "white" things, not the "black" things.
Sorry, but this thread has "no goal" !