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Determine if the improper integral converges or diverges 
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#1
Mar1213, 12:22 AM

P: 104

1. integrate from (1 to 3) of function (2) / (x2)^(8/3)
Can someone explain why this diverges. i do not understand it. when i plugged in the numbers there are no discontinuities and this is where i am stuck at. If there are no discontinuity does that means that it diverges? 2. Relevant equations 3. The attempt at a solution 


#3
Mar1213, 12:42 AM

P: 104

oh. it would equal to zero. so does that mean that it is continuous on the interval [1,3] except at 2? if so, do i proceed with solving it from 1,2 to 2,3 ?



#4
Mar1213, 12:44 AM

P: 548

Determine if the improper integral converges or diverges
Solve it from 1 to t, t to 3 and do the limit as t approaches 2 from the right and left.



#5
Mar1213, 01:09 AM

P: 104

i got the answer 12/5. Since its negative does that means that it diverges?



#6
Mar1213, 03:45 AM

P: 4

Graph the function in your head...as it approaches 2 the denominator (x2) term goes to zero, so the function goes to infinity. Hence the area under the curve also goes to infininity (diverges).



#7
Mar1213, 12:12 PM

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P: 3,171

In general, whether the integral diverges or not at a singularity depends on how "wide" the singularity is: the integral of ##1/x^p## over an interval including 0 will converge or diverge depending on the value of ##p##. Larger ##p## = wider singularity. 


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