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For this example it would be better to use a dummy variable (a variable just to help with solving the equation but isn't a part of the final answer). Let us say our dummy variable, t = 1+x^2. So, substitu...

This is a common question in C4 and the trick used to solve it is often used in sub-sections to full questions.

To solve it, we must simplify the expression in terms of cos(2x) using two trigonomet...

First we draw a picture, to visually see what the question is asking. A simple set of coordinate-axes and notches so we can accurately put our point P and Q, though being accurate isn't important it will ...

As there are 2 x terms in the integral we will use integration by parts. Remember;  ∫u*(dv/dx)dx =  uv -  ∫v*(du/dx)dx (found by integrating the product rule). From xcos(x) we need to decide which x term ...

The important part of this question is to really understand what the cosine function looks like, many students will use their calculators to find arccos(0.6) = 53.13 degrees, but not find the other soluti...