- #1

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**limits..proving they exist?**

Wot do u have to do to prove that an intergral exists.?? I know how to do it if the integrals bounds are given ( example, [a,b]) but wot if the integral is from x till infinity??

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- Thread starter saint_n
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- #1

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Wot do u have to do to prove that an intergral exists.?? I know how to do it if the integrals bounds are given ( example, [a,b]) but wot if the integral is from x till infinity??

- #2

Science Advisor

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integral of 1/x from a to b is log(b) - log(a), which tends to infinity as b tends to infinity so the integral doesn't exist.

integral of 1/x^2 from a to be is 1/a^2-1/b^2, which tends to 1/a^2 as b tends to infinity so the infinite integral exists.

If you wish to integrate from minus infinity to infinity, you must do the integral from a to b and let a and b tend to infinity independently.

Thus the improper integral of sin(x) over the real line does not exist even though you can choose the interval to be [-a,a] and get an answer of zero (other choices will give different answers hence the integral does not exist)

- #3

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How will you do

[tex]\int\frac{sinx}{x}dx[/tex]

from zero to infinity.

Which can be written as a alternating series

T subscript n =[tex]\mid\int\frac{sinx}{x}dx\mid[/tex] over intervals ([tex](n-1)\pi,n\pi[/tex])

but how do show as n tends to infinity that T(n) tends to 0?

cos i can't integrate it

[tex]\int\frac{sinx}{x}dx[/tex]

from zero to infinity.

Which can be written as a alternating series

T subscript n =[tex]\mid\int\frac{sinx}{x}dx\mid[/tex] over intervals ([tex](n-1)\pi,n\pi[/tex])

but how do show as n tends to infinity that T(n) tends to 0?

cos i can't integrate it

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