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To integrate the volume of revolution first imagine a thin disk around the x-axis which we want to know the volume of: Volume=area x height. The area of a circle is given by pi r^2 and in our case let us ...

Factorise the equation and then equate each set of brackets to 0 to obtain both possible solutions. 

By factorising: (x-6)(x-1)=0 

Therefore: x=6 or x=1

i) Well, if point P lies in AB, then the value of its x and y coordinates have to fulfill the condition imposed by equation AB. Therefore, substituting the x value p for x and the y value p+5 for y:

Since we are looking for a stationary this means the derivative will be equal to 0, so we will have to differentiate the equation. When we differentiate ( y = 2x + 27/x^2 ) we get ( dy/dx = 2 - 54/x^3 ). ...

This comes up in C4 in A level maths and differentiating it could come up in C3. You can write a^x as exp(ln(a^x))=exp(xln(a)) then differentiating this, you get ln(a)exp(xln(a))=ln(a)a^x. By differen...