Rhys_M
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Can somebody please help me find my mistake below? i've had to integrate by parts twice, in which i've had to do an integration by substitution.
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mqb2766
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At the end you forget to multiply by 2. The rest looks about right?
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Rhys_M
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(Original post by mqb2766)
At the end you forget to multiply by 2. The rest looks about right?
Oh duh of course.
I probably forgot that as I retried after plugging into an integral calc which had cosec in its answer so I was distracted trying to figure out where I should get that from - but i'll do the definite and check ans.

Update - the answer is pi/2 - pi²/2 + ln2 and mine gives pi/2 - pi²/2 + ln(root2/2)
Any ideas why? Thanks
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mqb2766
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The integrand
cosec^2(x)cot(x)
is undefined at 0 +/-k pi, so is the integral. around pi/2 shoud be ok?
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Rhys_M
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(Original post by mqb2766)
The integrand
cosec^2(x)cot(x)
is undefined at 0 +/-k pi, so is the integral. pi/2 shoud be ok.
Oh so if a term is undefined, the whole integral becomes undefined?
So simply ignore the pi/4 equation and the answer is -(pi/2 substitution) ???

Doing this makes the first 2 terms of my answer wrong tho, and the last term is still wrong (should be ln 2)
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mqb2766
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You can't find the area under a curve where it becomes undeffined?

I don't know what you're referring to with second part. Can you explain clearly / upload the working.
You're integrating pi/4 to pi/2 - its a bit blurred? What is the problem with that?
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Rhys_M
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(Original post by mqb2766)
You can't find the area under a curve where it becomes undeffined?

I don't know what you're referring to with second part. Can you explain clearly / upload the working.
You're integrating pi/4 to pi/2 - its a bit blurred? What is the problem with that?
Here's what I did:
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I took undefined as 0 which you have pointed out is wrong - what should I do for the definite integral?
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mqb2766
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Its correct apart from the ln() expressions. Yours should be negative, but otherwise theyre the same?
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the bear
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(Original post by Rhys_M)
Here's what I did:
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I took undefined as 0 which you have pointed out is wrong - what should I do for the definite integral?
you have not put a minus on the ln term when you expanded the second bracket
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Rhys_M
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(Original post by the bear)
you have not put a minus on the ln term when you expanded the second bracket
Thank you - I just realised 2ln(root2/2) is the same as ln2
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Rhys_M
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(Original post by mqb2766)
Its correct apart from the ln() expressions. Yours should be negative, but otherwise theyre the same?
Oh yea, I didn't realise ln2 is the same as 2ln(root2/2).
Thanks so much for your help
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