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HSC 2012-14 MX2 Integration Marathon (archive) (1 Viewer)

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braintic

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Re: MX2 Integration Marathon



Draw a picture for and sum areas.
I think you've somewhat overcomplicated this integral.

The integral is done in the 1st quadrant, so the absolute values are unnecessary.
And sin x + cos x integrates as it stands - there is no need to transform it.
 
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Re: MX2 Integration Marathon

I think you've somewhat overcomplicated this integral.

The integral is done in the 1st quadrant, so the absolute values are unnecessary.
And sin x + cos x integrates as it stands - there is no need to transform it.
Yeah you're right. works out the same.
 

seanieg89

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Re: MX2 Integration Marathon

1. Let u^2 = x
2. IBP



Next one



Let u^3 = sinx - cosx

3u^2 du = (cosx + sinx)dx

therefore,


problème

Pretty sure no elementary primitive exists. Can people please be more careful when posting questions?
 
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Re: MX2 Integration Marathon

problème

Use the property that makes it the integral of 0 to 2 f(x)+f(-x), then times the f(-x) by e^x on both sides and add the f(x) and f(-x) and factorise out the e^x +1, making it the integral of x^2?
 

Sy123

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Re: MX2 Integration Marathon

 

HeroicPandas

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Re: MX2 Integration Marathon

Use the property that makes it the integral of 0 to 2 f(x)+f(-x), then times the f(-x) by e^x on both sides and add the f(x) and f(-x) and factorise out the e^x +1, making it the integral of x^2?
yes
 

Sy123

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Re: MX2 Integration Marathon

Write as [1+5/(x+2)]^5 and expand.
Is there an easier method?
Oops, that is a typo, it should read (x+7)^5/(x+2)^7

Which can be resolved through substitution.

======

I'm running out of cool integrals =(
 

braintic

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Re: MX2 Integration Marathon

you could let u=x+2 which will still result in an expansion, although it will be slightly easier
Actually, its exactly the same - it just looks easier.
 

Makematics

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Re: MX2 Integration Marathon

Actually, its exactly the same - it just looks easier.
How? using my way i will have to expand (u+5)^5, while you will have to expand something with fractions, which are harder to deal with.
 

braintic

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Re: MX2 Integration Marathon

How? using my way i will have to expand (u+5)^5, while you will have to expand something with fractions, which are harder to deal with.
The fraction is still a unit that remains intact - it doesn't need to be broken up. As long as you think of the fraction as a variable itself, its exactly the same.
Seriously, if anyone sees expanding [1+5/(x+2)]^5 as being more difficult that (u+5)^5, they are going to struggle with a lot in Extension 2.
 
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