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Remember that the equation of a line is y=mx+c and m is the gradient of the line. The gradient of a perpendicular line will be the negative reciprocal of m ( that just means it will be -1/m). You can then...

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...