HSC 2017 MX2 Integration Marathon (archive) (2 Viewers)

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wu345

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Re: HSC 2017 MX2 Integration Marathon

stuck on this one, any ideas?

 

leehuan

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Re: HSC 2017 MX2 Integration Marathon

stuck on this one, any ideas?

The reverse quotient rule isn't obvious.

The denominator involves an odd power. Try making it an even power somehow.
 

Paradoxica

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Re: HSC 2017 MX2 Integration Marathon

Not only is this unnecessarily obfuscated, it's very difficult for the average MX2 student to comprehend.

Here's a more legible version of the problem.



The problem is remarkably trivial, when you come up with the correct substitution.

I'll leave it to Kingom.
 

Kingom

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Re: HSC 2017 MX2 Integration Marathon

Not only is this unnecessarily obfuscated, it's very difficult for the average MX2 student to comprehend.

Here's a more legible version of the problem.



The problem is remarkably trivial, when you come up with the correct substitution.

I'll leave it to Kingom.
 
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stupid_girl

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Re: HSC 2017 MX2 Integration Marathon

Not only is this unnecessarily obfuscated, it's very difficult for the average MX2 student to comprehend.

Here's a more legible version of the problem.



The problem is remarkably trivial, when you come up with the correct substitution.

I'll leave it to Kingom.
It is purposefully obfuscated but I think average MX2 student should be able to interpret it. End of the day, <f,g>w and <f,g> are just two real numbers. The answer would be the same if I call them star and moon, and ask for star/moon.

By the way, I think the condition a,b,k being positive cannot be dropped.
 

Paradoxica

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Re: HSC 2017 MX2 Integration Marathon

It is purposefully obfuscated but I think average MX2 student should be able to interpret it. End of the day, <f,g>w and <f,g> are just two real numbers. The answer would be the same if I call them star and moon, and ask for star/moon.

By the way, I think the condition a,b,k being positive cannot be dropped.
Wrong. k can be strictly less than -1, provided a and b are positive rationals with odd numerator.

Under the standard real definition of roots.
 
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EngineeringHelp

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Re: HSC 4U Integration Marathon 2017





Simplifying the derivative in Mathematica confirms the result.
Hey, sorry for being so bad at this subject, but how do you know to use that substitution? Thinking process? What are some key things to look out for when attempting a question?
 

Paradoxica

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Re: HSC 4U Integration Marathon 2017

Hey, sorry for being so bad at this subject, but how do you know to use that substitution? Thinking process? What are some key things to look out for when attempting a question?
Eliminate irrational functions using whatever you have at your disposal.

The only three ways of doing so are:

Classical Trigonometric Substitution (High School level)

Hyperbolic Trigonometric Substitution (University level)

Euler Substitution (Extracurricular)
 

EngineeringHelp

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Re: HSC 4U Integration Marathon 2017

Eliminate irrational functions using whatever you have at your disposal.

The only three ways of doing so are:

Classical Trigonometric Substitution (High School level)

Hyperbolic Trigonometric Substitution (University level)

Euler Substitution (Extracurricular)
Ooh, so for the HSC all i should worry about is a Trig Sub? As it wouldn't be right to be asked questions requiring the other two, right?
 

EngineeringHelp

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Re: HSC 4U Integration Marathon 2017

Also, does anyone have any 'not so complicated' reduction-formula questions? If so, please post. Im assuming Paradoxica will be supplying solutions xD <3
 
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