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First, let's assume that sqrt(2) is rational. That is, it can be expressed in the form a/b, where a and b are integers and the fraction is simplified as far as possible.
So we have sqrt(2) ...

A polar coordinate system is just another method to determine a position of a point in space just like the cartesian coordiante system does; which hopefully you are confident with now. At A-level all you ...

First thing to notice here is that this question tells us exactly what method they want us to use, subsitution, and what to substitute. Hence the first step is to turn the integral provided which is curre...

If the second derivative of an equation is positive (d²y /dx² > 0), we can see that this point on a curve is a minimum. This is because, where the first derivative finds the grad...

For integration by parts, the integral is uv - ∫ u' v dx. First we take u = ln x and v' = 1. While we could have u and v' be the opposite at this stage, it becomes apparent later on that we can't do this ...