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Re: MX2 2015 Integration Marathon Was the answer pi/4 ln(t^2)

Construct OP and OQ. Since midpoint of AB is P, then the line OP must be perpendicular to the chord (radii bisecting a chord is at a right angle, or a theorem like that). Therefore, angle APO = 90. This is similar with angle AQO. Since Q is midpoint of AC then OQ is perpendicular. Since angle...

Re: MX2 2015 Integration Marathon $ let $ u^{2} = x \\ 2udu = dx \\ I = \int{2u^2 e^{u}du \\ $ followed by IBP $

Re: MX2 2015 Integration Marathon New q: \int_{0}^{\pi} \cos^{2}(tan^{-1}(sin(cot^{-1}x)))

Re: MX2 2015 Integration Marathon $ let $ \cos^{-1}(x) = \alpha \\ cos(\alpha) = x \\ $Drawing a triangle, we can get all three sides relating to $ \alpha \\ $ Therefore, $ \int_{0}^{1} \sin({\cos^{-1}{x}) \\ = \int_{0}^{1} \sin(\alpha) \\ = \int_{0}^{1} \sqrt{1-x^{2}} \\ $ The integral can...

Re: MX2 2015 Integration Marathon wtf can someone edit my post or something that was my first attempt at latex

Re: MX2 2015 Integration Marathon \int_{0}^{100\pi} \sqrt{cos^{2}(x) + sin^{2}(x) - cos^{2}(x) + sin^{2}(x)} dx \\ \int_{0}^{100\pi} \sqrt{{2}} \sqrt{sin^{2}(x)} dx \\ int_{0}^{100\pi} \sqrt{{2}} \|sin(x)| \\ $Now, the graph of \|sin(x)| will repeat every pi/2 interval as it is a reflection of...

Re: MX2 2015 Integration Marathon I tried doing this by letting t = tanx and t^2 = tan^(2)x which you can then find sin^2x in terms of t. I got a logarithm function

Re: HSC 2015 4U Marathon 1/cosecx is just sinx

Re: HSC 2015 4U Marathon It is correct. But notice there is a +c. Sin^(-1)(x/4) and cos^(-1)(x/4) differ by pi/2. to prove this: d/dx sin^(-1)(x/4) + cos^(-1)(x/4) = 0 (cbb typing the differentation step) siince it equals zero and if two functions equal you can integrate. Int d/dx...

? Do I know you? What was the point of that post?

Can someone help me deconstruct these images a bit? I have no idea. I think the street philosopher has something to do with contextual power and authorial voice? I really don't know. Can someone help me please? also, the order is a bit messed up. The first two images should be swapped according...

Can someone help me deconstruct these images a bit? I have no idea. I think the street philosopher has something to do with contextual power and authorial voice? I really don't know. Can someone help me please? also, the order is a bit messed up. The first two images should be swapped according...

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