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Finding stationary points.

You can find stationary points on a curve by differentiating the equation of the curve and finding the points at which the gradient func...

Using integration by parts: split xcos(x) into x multiplied by cos(x). Differentiating x gives 1 and integrating cos(x) gives sin(x). The integral of xcos(x) can therefore be rewritten as xsin(x) - integr...

In theory, a monopoly is a situation in which the ‘industry is the firm’ however in reality in the UK we consider anything which controls 25% or more of the market to have monopoly pow...

Income can be defined as a flow of factor incomes, such as earnings, dividends and rent.  Alternatively, wealth is a stock of financial and real assets including savin...

Integration by parts formula: ∫ udv/dx = uv - ∫ du/dxv dx

To solve this problem we need to use a trick by thinking of lnx as lnx1
So we can choose: u=lnx, dv/dx=1
...