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HSC 2015 MX2 Integration Marathon (archive) (1 Viewer)

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mreditor16

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Re: MX2 2015 Integration Marathon

Really? By , I meant the derivative of . So in the second quoted post, basically only one "tedious" step is required, which is to solve a linear system of equations in two unknowns.

Once we do this, we're pretty much done, because the integral of the part is just .

i.e. , where (assuming I didn't make a silly mistake in solving the simultaneous equations, but you get the idea).

Then





.

I'd say that's not too messy.
Oh yeh it comes out nicely, I think I might have made some mistake along the way :/ But yeah that comes out neatly - thanks heaps Integrand :)
 

leehuan

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Re: MX2 2015 Integration Marathon

For 1 you could've just done...

 

leehuan

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Re: MX2 2015 Integration Marathon

I know :p

I had a long think about Q3. The hint the sheet gave was to use log laws but the fact that there is no standard result, it might not be suitable for Ext 2 maths anyhow... Don't see how the f(a-x) - f(x) trick will work either. I'll leave that question unless one of the experts can take care of it.
 

Drsoccerball

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Re: MX2 2015 Integration Marathon

I know :p

I had a long think about Q3. The hint the sheet gave was to use log laws but the fact that there is no standard result, it might not be suitable for Ext 2 maths anyhow... Don't see how the f(a-x) - f(x) trick will work either. I'll leave that question unless one of the experts can take care of it.
Could you do it doe?
 

leehuan

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Re: MX2 2015 Integration Marathon

Nope. I could only do this.
Screen Shot 2015-06-22 at 10.34.00 am.png



Note:

Possibly useful compound angle formula:
 

porcupinetree

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Re: MX2 2015 Integration Marathon

Next integral:

sqrt (1 + sin2x) dx
 

RecklessRick

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Re: MX2 2015 Integration Marathon

Next integral:

sqrt (1 + sin2x) dx
Idk how to LaTeX (can someone point me to a guide of some sort?) so here goes:

sqrt(1+sin2x)
= sqrt(1 + 2sinxcosx)
= sqrt(sin^2x + 2sinxcosx + cos^2x)
= sqrt((sinx + cosx)^2)
= sinx + cosx

so integral sqrt(1 + sin2x) dx
= sinx - cosx + c
 

porcupinetree

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Re: MX2 2015 Integration Marathon

Next question:

sqrt [(5-x)/(x-1)] dx
 

leehuan

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Re: MX2 2015 Integration Marathon

Instead of applying the 'not spoilered' identity immediately I would do this:



So that I can use integration by parts at where I cut off your quote.

NEXT QUESTION:
 
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