Why hello improper integral, how are you?

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SUMMARY

The discussion centers on evaluating the improper integral of the function 3/x² from -1 to 1. The user attempts to solve the integral by splitting it into two limits as t approaches infinity, but encounters an issue with the result being infinity. The key error identified is the integration across the singularity at x = 0, which is outside the domain of the function. The correct approach involves recognizing the improper nature of the integral and adjusting the limits accordingly.

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Homework Statement


integral from -1 to 1 of 3/x^2 dx


Homework Equations





The Attempt at a Solution


Limit
t --> infinity integral from -1 to t of 3/x^2 dx + limit t --> infinity integral from t to 1 of 3/x^2 dx

Limit
t-> infinity -3/t - (-3/-1) + Limit t--> inifinty (-3/1) - (3/t)

-3 -3 = -6

Now when I check the answer in my calc I get infinity. Thus my answer is probably wrong. Where did I go wrong?
Thanks so much =]
 
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Why infinity? It is (a) outside the domain, and (b) you are integrating across the singularity.
 
yeahyeah<3 said:
Now when I check the answer in my calc I get infinity. Thus my answer is probably wrong. Where did I go wrong?

Limit
t --> infinity integral from -1 to t of 3/x^2 dx + limit t --> infinity integral from t to 1 of 3/x^2 dx

This should be as t→0.
 

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