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Re: MX2 2016 Integration Marathon Test http://i0.kym-cdn.com/photos/images/original/000/002/116/Longcat_War.jpg

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\\ $If you prefer a more explicit answer, you may like to let $d=\left [ - \frac{7\pi}{6},\frac{\pi}{6} \right ]. $ Then the domain is $ D=d+2k \pi, k \in \mathbb{Z}.

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I've never understood them to be honest.

Re: MX2 2016 Integration Marathon They can use their curve sketching techniques (the section on absolute values) to quickly sketch the curve and then work with the integral from there.

Re: MX2 2016 Integration Marathon \\ $To add to the marathon, find $ \int \frac{x^2-1}{x^3+x}dx

Re: MX2 2016 Integration Marathon Let the original integral be I_1, then define I_2 to be the same except with cos in the numerator. I_1 + I_2 = .... I_1 - I_2 = .... Solve simultaneously. Rationale: The expression is semi-symmetric, so we can somehow force a more 'complete' symmetry...

Re: Extracurricular Integration Marathon Pretty much. Though for that question we'd use a combination of the polar and cartesian systems to evaluate it. In the Volumes problem Q14 of 2014 BOS Trials Extension 2, I provided a VERY brief glimpse into evaluating that integral via double...

Re: Extracurricular Integration Marathon Typically it's taught in an first course in vector calculus, not linear algebra where matrices tend to live. The initial treatments tend to be highly elementary in nature and are very much as you have described above. A Year 11 student could compute...

Re: Extracurricular Integration Marathon You're probably clever enough to get the general gist of it (double integration via Cartesian coordinate system) from this image. I'm guessing you just want a rough idea, not a more rigorous construction. Just imagine throwing in an extra dimension to...