I want to proof:

I did it in two different way as shown below:

(1) Let

BUT

(2) Let

Obviously the two ways give different result. What happened?

Thanks

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- Jul 25th 2013, 08:53 AMAlan0354Question of change of variables in definite integral.
I want to proof:

I did it in two different way as shown below:

(1) Let

BUT

(2) Let

Obviously the two ways give different result. What happened?

Thanks - Jul 25th 2013, 09:16 AMHallsofIvyRe: Question of change of variables in definite integral.
Going from to is adding NOT .

because and for all m. - Jul 25th 2013, 10:52 AMAlan0354Re: Question of change of variables in definite integral.
- Jul 25th 2013, 12:26 PMBobPRe: Question of change of variables in definite integral.
The limits for the second transformation are wrong aren't they ?

If

then

Your problem, as I see it, is caused by your use of the same symbol for both the original and the transformed variable. What you have done, is to use the transformation for the integrand, but the transformation for the limits. - Jul 25th 2013, 03:02 PMAlan0354Re: Question of change of variables in definite integral.
- Jul 26th 2013, 02:38 PMBobPRe: Question of change of variables in definite integral.
You seem to be going out of your way to confuse yourself, and you're still making the same mistake.

For your last calculation, you are now using as the 'original' variable and as the 'transformed' variable and the relationship between them is

For the stuff to the right of the integral sign is being replaced by

If you use the same replacement method for the limits, as you must, then you have to say that,

when then is given by That is,

Similarly when

The limits