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Re: HSC 2013 4U Marathon Ah yeah oops :P

Re: HSC 2013 4U Marathon $The polynomial$ \ \ P(x) \ \ $has integer co-efficients$ p+\sqrt{q} \ \ $is a root of the polynomial, where$ \ \ p, q\ \ $are rational$ $Prove that$ \ \ p-\sqrt{q} \ \ $must also be a root of the polynomial$

Re: MX2 Integration Marathon \int \sqrt{\frac{e^x-1}{e^x+1}} \ dx

Re: MX2 Integration Marathon u^3=x I=3\int \frac{(1+u)^{1/4}}{u} \ du m^4=1+u I = 3\int 4 + \frac{4}{m^4-1} \ dm I = 3 \int 4 + \frac{1}{m-1} - \frac{1}{m+1} - \frac{2}{m^2+1} \ dm I = 12m + 3\ln(\frac{m-1}{m+1}) - 6\tan^{-1}m + c I = 12(1+x^{1/3})^{1/4} + 3\ln...

Re: MX2 Integration Marathon Do people want to use this thread too specifically for integration?

Re: HSC 2013 4U Marathon 1. P'(x) = (2x-(a+b))g(x) + g'(x) (x-a)(x-b) If a and b are consecutive roots, then it is easy to see that P'(a) and P'(b) are opposite in sign by drawing a picture. They can't be zero since they have roots of multiplicity of 1. P'(a) = (a-b) g(a) P'(b) = (b-a)...

Re: HSC 2013 4U Marathon $i) Prove that$ \lim_{z \to 0} \int_z^{\pi/2}\ln(\sin x) \ dx = \lim_{z \to 0} \frac{1}{2}\int_z^{\pi/2} \ln(\sin(2x)) \ dx - \frac{\pi}{4} \ln 2 $ii) Explain why$ \lim_{z \to 0} \int_z^{\pi/2} \ln(\sin(2x)) \ dx = \frac{1}{2} \lim_{z \to 0} \int_z^{\pi} \ln(\sin...

re: HSC Chemistry Marathon Archive The Photomultiplier from Atomic Absorbtion Spectroscopy?

Re: HSC 2013 4U Marathon YEp something like that, nice work.

Re: HSC 2013 4U Marathon $Evaluate$ I=\int_0^{\frac{\pi}{2}} \frac{\sin^2 x}{1+\sin(2x)} \ dx

Week 1: English 1 and 2 Week 2: Tuesday: MX2 Friday: Economics Week 3: Tuesday: EX1 =( Wednesday: Chemistry Friday: Physics All my worst subjects in the same week :/

Re: HSC 2013 4U Marathon lol I got owned

Re: HSC 2013 4U Marathon (;

Re: HSC 2013 4U Marathon $Find$ \int_{-9001}^{9001} \sin(x^3) e^{-\pi^{77} x^{14}} \tan^{-1}(\ln(x^2)) (x^{191919923134}-1) \ dx

Re: HSC 2013 4U Marathon Ah yes ok.

Re: HSC 2013 4U Marathon Thank you =) That way people who browse this thread who don't know how to do it at least get a solution.

Re: HSC 2013 4U Marathon I would have accepted the answer with only the above sentence ^^ =========== $Find for all values of$ \ \ \alpha \int \frac{dx}{x^{\alpha + 1} + x}

Re: HSC 2013 4U Marathon The constant term does not cancel out. I think you have made a silly mistake.

Re: HSC 2013 4U Marathon How?

Re: HSC 2013 4U Marathon We do not know that M is the centre.