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Integration with trig identites qs


Arjen
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IMG 20200315 WA0003

 

Question 8, I'm not sure how to even start the qs

Please show working I would be very grateful

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Abdurrahman
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@arjen i used integration by parts but just got lost along the way ? ? 

 

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Further_Maths_Student
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9D930630 D222 4693 A5A1 01D4E5EAB36A

I would start it like this 

by parts, then you might have to do by parts two more times

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Abdurrahman
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@further_maths_student yeah i started in a similar way, however my "v" is different to yours, how did you get v? Are you sure its correct because I got v = 1/2(cot(x))^2 (+c) using inspection as well as substitution to double check. But other that, your absolutely right! Thank you man!! ? 

 

 

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Abdurrahman
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@zeeshan @zubair sir could you please have a go? 

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Further_Maths_Student
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 @abdurrahman

your v is fine, both of ours differentiate to give cosec^2x cotx. 

I got v by inspection (reverse chain rule) so if you differentiate -cosec^2x, you will get 2cosec^2xcotx (i pretended the 2 was with the trig functions instead of being with x^2, and I just realised that i made a mistake because I wrote positive cosec^2x. I’m gonna send the solution I wrote anyway but keep in mind there are sign errors

9E69CF21 A78E 46B7 9E6C 9A45CBDFAEE2
1694242A 6F70 455F 8B36 A86637461B8F

Then by parts again of the new integral 

0A7C6446 C64B 4FEE BB04 391B9A1CF1E5

And we get

A03CC334 428C 453E 9433 8ED7391DE39E

And finally 

CA6017BD B5C2 4BAC 954E 74CDC25C6DB7

 

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Arjen
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@further_maths_student

 

Thanks a lot, made a lot of sense!

 

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Abdurrahman
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My final integral that I got which im pretty sure is wrong is: 2x^2cot^2(x)4xcot(x)cosec^2(x)

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