HSC 2015 MX2 Integration Marathon (archive) (5 Viewers)

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leehuan

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Re: MX2 2015 Integration Marathon







No plus sign at the end
 

VBN2470

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Re: MX2 2015 Integration Marathon

^ I think using the direct substitution would have made the first part a bit easier (no need for a second substitution). Rest looks fine though :)
 

leehuan

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Re: MX2 2015 Integration Marathon

^ I think using the direct substitution would have made the first part a bit easier (no need for a second substitution). Rest looks fine though :)
I would like to agree :D
 
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VBN2470

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Re: MX2 2015 Integration Marathon

 
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FrankXie

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Re: MX2 2015 Integration Marathon

but the borders will be from pi/4 to pi/2 and when you get uv, you have to sub theta = pi/2 and that gives infinity
no, at pi/2, you still get finite, actually zero ( by multiplying cos^n both numerator and denominator )
 

VBN2470

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Re: MX2 2015 Integration Marathon

^ Yep,
 
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VBN2470

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Re: MX2 2015 Integration Marathon

Use the "plus 1 minus 1" trick to split the integrand and apply IBP once to get
 

Ekman

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Re: MX2 2015 Integration Marathon

Next Question:

 
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