Cambridge Prelim MX1 Textbook Marathon/Q&A (2 Viewers)

Paradoxica

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Find d/dx ( x^2logx) ... = 2xlnx + x

Hence evaluate Integral from 1 to e xlnx dx

I get the answer : (e^2 + 1)/4

Could someone see if they get the same result.

The answer says its (e^2 - e + 1)/ 2

Still can't figure where I have gone wrong.




 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Consider the curve y = -xlnx + 4

Given that y'' < 0 for all values of x in the natural domain. What is the natural domain and range of the curve??
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread





 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Given that k is an even integer, find Integral from -2 to 2 x(e^x)^k dx
 

leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Given that k is an even integer, find Integral from -2 to 2 x(e^x)^k dx
Are you sure this is 3U and there was no precursor? Because I would've also used IBP here (except for, as pointed out, the specific case of k=0)
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Yes it is 3U and no precursor question , and what is IBP?
 

leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

This is what happens when InteGrand is not here.
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Yes it is 3U and no precursor question , and what is IBP?
IBP stands for Integration by Parts, an integration technique taught in HSC 4U Maths.
 

leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

IBP stands for Integration by Parts, an integration technique taught in HSC 4U Maths.
Do you have a 3U method for this question?
 

leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I know. Wolfram Alpha refuses to return a more elementary solution,and I can't think of anything.
You accidentally mucked up your degenerate case btw. That integral is 0
 

leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

This is so stupid. No definite integral tricks work here either, and we don't have an odd function to manipulate.

applei, exercise + question number please...
 

Paradoxica

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

This is so stupid. No definite integral tricks work here either, and we don't have an odd function to manipulate.

applei, exercise + question number please...
The integral itself, when treated as a function, is odd though. However, I fail to see how this will help us prove the formula for the definite integral.
 

leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

xe^(x^k) will go into odd functions by default, yep
 

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