Partial fraction integration question (1 Viewer)

[yjhere]

Integrate 40/(400-v^2) by dv.

I get = 40 integral 1/(20-v) by dv + 40 integral 1/(20+v) by dv
= 40 ln (20+v)/(20-v).

The answer is ln (20+v)/(20-v) without the 40. Can somebody tell me what happened to the 40?
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[Carrotsticks]

You did your partial fractions incorrectly. If you re-group your partial fraction decomposition, you will see that it's not the same thing.

 

[iStudent]

after doing partial fractions, i got A = 1/40 and B = 1/40 (the constants on top)
when integrating, this is factored out, so it cancels with the 40 you got
and the answer becomes: ln(20-v) + ln(20+v)
or ln(20+v)/(20-v) after rearranging

 

[yjhere]

Oh wow can't believe I totally skipped everything. Thanks guys!

 

[RealiseNothing]

A little tip when dealing with partial fractions like these. Consider the general form of the result, if we work backwards we can easily see what happens to the 40 on top:







So in your question, we can see from the denominator that since then , and so the numerator is . This means that the 40 will in fact be A PART of the partial fractions process, and so there is no need to factor it outside of the integral.