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HSC 2016 MX2 Integration Marathon (archive) (1 Viewer)

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leehuan

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Re: MX2 2016 Integration Marathon

Something must've went wrong to get the negative answer but I'm too tired to check.



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InteGrand

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Re: MX2 2016 Integration Marathon

Something must've went wrong to get the negative answer but I'm too tired to check.



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6 pages...now that is one tedious integral!
 

leehuan

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Re: MX2 2016 Integration Marathon

Found my mistake, in the last page line 3, the pi/2 ln(2) should be negative. Hence at the end pi/2 ln(2) is positive.

Otherwise, yay wolfram alpha agrees!
 

InteGrand

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Re: MX2 2016 Integration Marathon

Is this just a typo (and doesn't affect the rest of the working)? (The second fraction on the R.H.S. is just 0.) Ceebs carefully reading through the whole thing haha.
 

Drsoccerball

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Re: MX2 2016 Integration Marathon

Is this just a typo (and doesn't affect the rest of the working)? (The second fraction on the R.H.S. is just 0.) Ceebs carefully reading through the whole thing haha.
:O my nigga
 

Sy123

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Re: MX2 2016 Integration Marathon

Is this just a typo (and doesn't affect the rest of the working)? (The second fraction on the R.H.S. is just 0.) Ceebs carefully reading through the whole thing haha.
Yep the second term on the numerator is just 3/2, changed, (didn't affect rest of the working)
 

leehuan

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Re: MX2 2016 Integration Marathon

Can I just give the 16'ers something at a reasonable difficulty...

 

leehuan

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Re: MX2 2016 Integration Marathon

Hint: Double and Triple Angle identities.
Triple angle identity is the clever way to finish the integral. But in the scope of the 4U course unless they ask for it to be derived first using compound angles, the 4U approach to sin^3 is using a Pythagorean identity instead
 

Drsoccerball

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Re: MX2 2016 Integration Marathon

Or you can create a reduction formula for
 
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