Intergration using partial fraction, simplification

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tande33
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Report Thread starter 4 weeks ago
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Hi,
Question: https://isaacphysics.org/questions/p...8-6bcea2b383af

What is the issue: Well I think I have done the integration right but I am stuck on simplifying the final answer (as this is what the website is suggesting)
I came out with the answer :

1/(b-a) * ln |(a+b)/a| + 1/(a-b) * ln (2)

I have tried combining logs but the question suggests it is not in the right form. Any ideas? Many thanks in advance

I am happy to post working to get to that answer if necessary, I haven't done it yet as its quite long!
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ghostwalker
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(Original post by tande33)
Hi,
Question: https://isaacphysics.org/questions/p...8-6bcea2b383af

What is the issue: Well I think I have done the integration right but I am stuck on simplifying the final answer (as this is what the website is suggesting)
I came out with the answer :

1/(b-a) * ln |(a+b)/a| + 1/(a-b) * ln (2)

I have tried combining logs but the question suggests it is not in the right form. Any ideas? Many thanks in advance

I am happy to post working to get to that answer if necessary, I haven't done it yet as its quite long!
Agree with your answer. So, assuming we didn't both make the same mistake, you could combine the ln(2), into the first part to get:

\displaystyle\frac{1}{b-a}\ln\left| \frac{a+b}{2a}\right|

Can't think of anything else useful you could do to it.
Last edited by ghostwalker; 4 weeks ago
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tande33
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Report Thread starter 4 weeks ago
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(Original post by ghostwalker)
Agree with your answer. So, assuming we didn't both make the same mistake, you could combine the ln(2), into the first part to get:

\displaystyle\frac{1}{b-a}\ln\left| \frac{a+b}{2a}\right|

Can't think of anything else useful you could do to it.
Thanks, that worked, not sure why I didn't try that, Bit random, but I was just wondering if the Weierstrass substitutions are part of a level maths (or further maths), I came across them recently and was curious.
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ghostwalker
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(Original post by tande33)
Thanks, that worked, not sure why I didn't try that, Bit random, but I was just wondering if the Weierstrass substitutions are part of a level maths (or further maths), I came across them recently and was curious.
Certainly used to be, but I can't say for sure. Others on here, familiar with the syllabus, should be able to confirm/deny. Otherswise checking your board's syllabus online would be the way to go.
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