Search over 10,000 free study notes

While I doubt students will ask this exact question, think it provides the basis for what are usually the most difficult questions in GCSE papers, and students would usually be unsure where to start. My i...

First use the substitution to find du/dx which is 2x. From this we now know that dx= du/2x (just re-arranging.) Substituting that into the integral we now get (6x³+4x)/ (sqrt (u) x 2x) du. Canc...

Although it can be tempting to dive straight into such a question, its always useful in mathematics to take a step back and assess the question before scribbling down panicked answers.

For inst...

This question often throws maths students off fairly easily as they are generally not taught the integral of lnx, and do not usually realise that integration by parts can be used for anything, as you can ...

Firstly, we need to differentiate the equation to find an equation for the gradient of the line.dy/dx = 6x-12We know the original graph was quadratic, and therefore only has one stationary point. This is ...