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Firstly, integrate each term individually, starting off with the 3x^4. In order to integrate the index on the x term needs to be raised by 1, and the coefficient of the x should be divided by this new val...

To start off, let's write the equation involving these three objects: Mv = xv. Now, looking at the first form of the equation, we don't want any eigenvector to have all its entries be zero, or else the ei...

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 ...