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x² + 10x + 24 = 0
First we must factorise the equation, which means put it into brackets. To do this we must find two numbers which multiply to equal 24 and add together to make 10. The on...

A + B + C = £722A = B3B = C0.5 B + B + 3B = £724.5 B = £72B = £16C = £48

The first thing to do is write down y’ and y’’ neatly since these are the main two equations we will be working with… y’ = 2x² – x – 3 & y’’ = 4x – 1… To find the stationary point we must f...

Check the equation is in the form dy/dx + P(x) y=Q(x) (show example) Find the int factor: I(x)=e^{integralP(x) dx}Multiply all terms by the integrating factorMake sure you show this step clearly: ...

We can use the formula for a Volume of Revolution: V =π ∫ (e^x + e^(-x))^2 dx, with limits x = 0, x = ln4.Expanding the brackets: (e^x + e^(-x))^2 = e^2x + 2 + e^(-2x).So: V = π ∫ (e^2x + 2 + e^(-2x)) dx ...