Question 362177
<font face="Garamond" size="+2">


These integrals are improper because you have to calculate them as a limit.  You cannot calculate


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \int_a^\infty\ f(x)dx]


directly. You must calculate:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \lim_{b\rightarrow\infty}\,\int_a^b\ f(x)dx]


From a table of integrals:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \int\ xe^{cx}dx\ =\ \frac{e^{cx}}{c^2}\left(cx\ -\ 1\right)]


Substitute *[tex \Large c\ =\ -3] and replace the upper limit with an arbitrary variable, say *[tex \Large a] and then take the limit as *[tex \Large a] increases without bound.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>