Calculate the generalized integral
Attachment 14469
Attachment 14470
Am I correct? and then?
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Calculate the generalized integral
Attachment 14469
Attachment 14470
Am I correct? and then?
Quote:
Originally Posted by sf1903
Sorry to say but you're not even close to correct, and if you wrote the above then I think you need to go back to your general basics on integration:
$\displaystyle \int\frac{x^2-1}{x^4}dx=\int\left(\frac{1}{x^2}-\frac{1}{x^4}\right)dx=-\frac{1}{x}+\frac{1}{3x^3}$.
Now evaluate the above in the integral's limits and make the upper limit tend to $\displaystyle \infty$ ...the answer must be $\displaystyle \frac{2}{3}$
Tonio
we can also turn this improper integral into a proper one, so let's put $\displaystyle x=\frac1t$ and the integral becomes $\displaystyle \int_{0}^{1}{\left( 1-t^{2} \right)\,dt}=1-\frac{1}{3}=\frac{2}{3}.$
