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    • Thread Starter
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    Hi,

    I have just done about three questions all working out whether the integrals converge or diverge:

    ∫dx/((x+4)(5x+1)) between infinity and zero
    ∫dx/x(1+x^2) between 1 and 0
    ∫dx/x^2(1+x^2) between 1 and 0

    I have tried working them out by splitting them all into partial fractoins etc. but i am not sure if my answers are right, is there a quick way of checking my answers?

    thanks
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    post your answers?
    • Thread Starter
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    for the second and third ones i got that they both tended towards infinity as delta tends towards 0+ so they both diverge?

    For the first one i got stuck
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    First one has an exact answer.
    • Thread Starter
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    i got as far as -1/19[ln(R+4/5R) -ln4) im not sure if thats right?

    Also do you know if the last two both tend to infinity and diverge?

    Thanks
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    The second and third both diverge since you have an infinity of order greater than or equal to one in the denominator .
    • Thread Starter
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    right thanks so im right that the last to tend to infinity and so diverge

    but with the first one will i not just get that it diverges because does ln(R+4/5R) not tend to infinity as R tends to infinity?
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    (Original post by sonic7899)
    right thanks so im right that the last to tend to infinity and so diverge

    but with the first one will i not just get that it diverges because does ln(R+4/5R) not tend to infinity as R tends to infinity?
    No it wouldn't.

    Dodgy maths warning below before I get told off:

    Try investigating it on your calculator using increasingly large values for R.

    As R approaches infinity, you can effectively ignore the +4 bit.

    What do you think the value of ln((R+4)/5R) might tend towards now?

    If you are still not sure, break up the logarithm:

    ln((R+4)/5R) = ln (R+4) - ln R - ln 5

    Does that help?
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    yeh i think so, the whole thing will tend to -1/19[ln5-ln4] btw should what you but above not be (lnR + ln5)?
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    sorry to be a pain but can someone confirm this lol its driving me mad
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    anybody???
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    you should find it tends to 1/19[ln5 + ln4] i.e 1/19 ln20 check your workings for a sign error
    • Thread Starter
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    thanks
    • Thread Starter
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    i think the 1/19 has to be negative doesn't it because that comes from splitting the original expression in to partial fractions so surely -1/19[ln5-ln4] is correct?
 
 
 
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