www.imgur.com/nGjEjX8
www.imgur.com/O3sZNpH
EDIT: That final c should be swapped with a k, but I can't be bothered to edit it and upload another photo.
Last edited by calamebe; 13 Dec 2016 at 5:21 PM.
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Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
Last edited by juantheron; 23 Dec 2016 at 6:19 PM.
I hope this one isn't too bad.
“Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
― Brandon Mull
This definite integral must be positive because the integrand is a complete square.
(Sorry for the typo in numerator this afternoon.)
Last edited by stupid_girl; 28 Dec 2016 at 10:54 PM.
61root(2)/840 right? What I did was break up the sin part, get three different integrals, one of which is easy to work out, then for the other two I created a recursion formula for the integral of sec(x)^n from 0 to pi/4, and added/subtracted the three integrals, and got that. I might post working, but it is unbelievably messy.
HSC 2017
Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
Sorry it's my fault. I accidentally missed out the exponent on the numerator when I typed it in latex.
Nevertheless, the mistyped integral is not messy. I just attempted it and the integrand can be broken into 0.5 sin x/(cos x)^7 and -0.5(sec x)^6. Substitue u=cos x and u=tan x respectively.
Last edited by stupid_girl; 29 Dec 2016 at 12:38 AM.
Well this one is 22/7 - pi, I just did some algebra to break down the expression to tan(x)^4(1-tan(x))^4, made a substitution u=tanx and just some relatively easy integration from there. I did have to use the binomial theorem in the last integral though, I feel like there would be a more elegant way to do it.
HSC 2017
Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
This is of course a proof that 22/7 > pi.
This question relies on Fundamental Theorem of Calculus and substitution.
http://imgur.com/a/YGobh
I hope that is clear enough. If not I'm trying to learn LaTeX so if it's too blurry/messy I can transcribe it to be readable haha.
HSC 2017
Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
http://imgur.com/a/YGobh
I hope that is clear enough. If not I'm trying to learn LaTeX so if it's too blurry/messy I can transcribe it to be readable haha.
HSC 2017
Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
http://imgur.com/a/QAcfP
I feel as though my method is very convoluted, is there a much easier way?
HSC 2017
Physics, Chemistry, Biology, English Advanced, Japanese Continuers
HSC 2016
Mathematics Extension 1, Mathematics Extension 2
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