HSC 2012-14 MX2 Integration Marathon (archive) (2 Viewers)

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braintic

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Re: MX2 Integration Marathon

It is likely that I made a mistake but here goes... Also I skipped a few steps (IBP of sec^3theta dtheta) to save some time.



Correct. But you don't need the absolute value.
 

braintic

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Re: MX2 Integration Marathon

In HSC you don't need it. But absolute value is most correct.
No, I mean you don't need the absolute value in THIS question, whether or not the HSC generally requires it. The thing you are trying to find the absolute value of CANNOT be negative.
 

Sy123

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Re: MX2 Integration Marathon

Is there a USYD Integration Bee?

 
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Re: MX2 Integration Marathon

I don't think there is a Usyd Integ Bee...
 

Sy123

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Re: MX2 Integration Marathon

This is a great integral, a little long and the answer isn't very elegant, but the path towards it is I think.

 

Sy123

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Re: MX2 Integration Marathon

care to share a solution? :)
Ok:









Make a right angled triangle, we get that:





Replacing the bottom trig identities with the appropriate forms for u.





Then expand, the middle term can be integrated into something to do with sine inverse.
The first term and the last expanded can be dealt with using a sine substitution.

Very straightforward from there.


EDIT: On hindsight I think I could greatly shorten the length of this solution, perhaps by splitting the fractions of trig integral straight away.
 
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Makematics

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Re: MX2 Integration Marathon

Ok:









Make a right angled triangle, we get that:





Replacing the bottom trig identities with the appropriate forms for u.





Then expand, the middle term can be integrated into something to do with sine inverse.
The first term and the last expanded can be dealt with using a sine substitution.

Very straightforward from there.


EDIT: On hindsight I think I could greatly shorten the length of this solution, perhaps by splitting the fractions of trig integral straight away.
wowzer haha thanks that's pretty cool.
 

Sy123

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Re: MX2 Integration Marathon



 
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