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As you will be aware, it is not easy to directly integrate terms involving sin^2(x) and cos^2(x), so we use a substitution to turn them into something which we can integrate.

From the double a...

The integration by parts formula takes the form:

int(uv') = uv - int(vu') 

where v' = dv/dx and u' = du/dx

A lot of the art of using the integration by part...

Firstly, what are we trying to achieve by differentiating a function? Differentiation allows us to compute the rate of change of a function at any point along ...

The chain rule is most commonly seen in Leibniz's notatio...

The maximum/minimum of a function are the points where the first derivative (the gradient) of the function is zero.

So with a function of the form y=f(x), you must take the derivative (dy/dx) ...