- #1

Runei

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**Trigonometric substitution - Why?**

Hey guys

Im sitting here with trigonometric substitution problems, and I have a kind of a problem.

I can't see WHY it is legal to substitute x for a sin ([tex]\theta[/tex])

If you have a the integral:

[tex]\int[/tex][tex]\frac{1}{\sqrt{1-x^2}}[/tex]dx

Then I know the substitution would be

x = sin([tex]\theta[/tex])

But from where I see it, and I guess that is the problem, if the integral is just provided in the form it is above, then x [tex]\in[/tex][tex]\Re[/tex]

Then why can we substitute x by the function g([tex]\theta[/tex]) = sin ([tex]\theta[/tex]) when

g([tex]\theta[/tex]) [tex]\in[/tex] [-1 ; 1]. From my point of view there is a problem when the function we substitute by only gives and small fraction of the possible inputs x can have...

Anyone follow my thoughts? Someone can explain it?

regards,

Rune

Engineering Student