## Gaussian Integral Substitution

$$\int_{-1}^{1}e^{x}dx$$

Then performing the substitution $x=\frac{1}{t}$ would give me

$$\int_{-1}^{1}-e^\frac{1}{t}t^{-2}dt$$

Which can't be right because the number in the integral is always negative. Is this substitution not correct?

Sorry if I am being very thick but I can't figure out why I can't evaluate this simple integral with this change of variables.
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hi pcvrx560!
 Quote by pcvrx560 … Is this substitution not correct?
the substitution is fine, but the limits are wrong …

as x goes up from -1 to 1,

t (= 1/x) goes down from -1 to -∞, and then from +∞ down to 1 …

you'ld need to write ##\int_{-1}^{-\infty} + \int_{\infty}^{1}##
(or ##-\int^{-1}_{-\infty} - \int^{\infty}_{1}##)
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## Gaussian Integral Substitution

Thanks, tiny-tim! That cleared it up for me.

I didn't think about the range I was integrating over, I was just mindlessly plugging numbers into 1/t.

 Tags calculus, change of variables, integratation