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Re: MX2 2015 Integration Marathon Is there a formal proof for that?? If 'c' is a constant independent of x, then you can just bring it out of the integral

Re: MX2 2015 Integration Marathon lol that's a very articulate proof

Re: MX2 2015 Integration Marathon How wouldyou prove that it's the same besides using substitution: u = pi/2 - x?

Re: MX2 2015 Integration Marathon Ah that's cool Thanks

Re: MX2 2015 Integration Marathon Why is I = int 0 to pi/2 ln(sinx)dx = int 0 to pi/2 ln(sin2x) dx ?

Re: MX2 2015 Integration Marathon I've seen people do it by using int f(pi/2 - x) = int f(x) giving I = int 0 to pi/2 of ln(costheta) dtheta Then adding, giving 2I = int 0 to pi/2 of ln(sin2theta) - ln2 dtheta Then using u = 2theta, 2I = int 0 to pi of ln(sinu) - ln2 du And then they...

Ahh, so that's why I got theta to be greater than pi radians?

Thanks But the answer is A. It didn't have to go through the centre. And also, was just wondering why I got the result I did as stated in the OP. edit: it was B so ur correct

Theta is the one at the centre facing 5y

community.boredofstudies.org/attachments/13/mathematics-extension-1/30632d1404894953-ruse-2013-trial-solutions-2013-jrah-extn1-trial.pdf Q9 Firstly, I use 2pi*r = circumference = 9y Gives me r = 9y/2pi Then Constructing a chord to complete the triangle, I then construct the radius from the...

Re: HSC 2015 4U Marathon Let u = pi/2 - x for both integrals LHS integral = int from -pi/2 to pi/2 of cos^8 x dx > 0 as it is even. RHS integral = int from -pi/2 to pi/2 of sin(4pi - 8x) = -sin8x dx = 0 as it is odd Holds true

Re: HSC 2015 4U Marathon So like a conjugate bar for complex numbers?

he ded

Re: HSC 2015 2U Marathon oh lol thanks. don't know why I only added it

Re: HSC 2015 2U Marathon How did you know f(x) was linear? It could have been something like a cubic and the x^3 could just cancel each other out edit: nevermind, the coefficients are different so there's no way x^3 could cancel out. Wondering if there's an alternative method to this question...

Re: HSC 2015 4U Marathon $ Let a number be in the form: $ a_n a_{n-1} ... a_1 a_0 $ where $ a_n $ is the 'n'th digit $ a_n a_{n-1} ... a_1 a_0 = a_0 + 10*a_1 + 100*a_2 + ... + 10^{n-1}a_{n-1} + 10^{n}a_{n} = a_0 + (9+1)a_2 + ... + (9+1)^{n-1}a_{n-1} + (9+1)^{n}a_{n} = a_0 + (9+1)a_2 +...

Re: HSC 2015 2U Marathon Let y = 3^x Eqn turns into y^2 + 2y - 15 = 0 Solve as a quadratic for y And then equate to 3^x Reject any negative y values by noting that 3^x > 0 for all real x

oh i was in your truongs class before

Would anyone who's done it or experienced the paper have an idea of what the cutoff for e4 and/or state rank is? Thanks

lol random advertisement to an instagram on a math thread on boredofstudies