what is the meaning of improper integral?

improper integrals are integrals that cannot be evaluated like you would evaluate a normal integral. The classic example is \[\int\limits_{1}^{\infty} 1/x^2\]

instead you have to evaluate the improper integral by replacing the infinity with a variable, doing the integral, and then taking the limit of the result as the variable goes to infinity

Note: not all improper integrals have an answer. Most improper integrals go to infinity. This makes sense when you think about how an integral is the sum of the area under the curve. If you add up the area under the curve over the distance to infinity, the curve has to approach zero.

online notes on this can be found at http://tutorial.math.lamar.edu/Classes/CalcII/ImproperIntegrals.aspx

You mean the improper integral is the sum of the area the curve, therefore..the limit is approaches to zero.doing the integral, the limits became infinity?? can you give me an example that the limit is infinity??

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