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In this question we will use the fact we know a straight line can be written in the form (y-y₁)=m(x-x₁). Where m is the gradient and (x₁,y₁) is a point on the l...

Derivatives can be used to work out rates of change of non-linear systems which are encountered everyday. Moreover derivatives allow us to describe the shape of a function.

equation of a circle: (x - a)^2 + (y - b)^2 = r^2, where the circle has centre (a, b) and radius r.
Let's draw the diagram, where (x, y) is some point on the circle, which for ease we'll call P, and...

Use integration by parts, by setting u=x and cos(x)=dv/dx. The final result should be xsinx + cosx + c.

we must integrate (4cos⁴ x-4cos² x+1)^1/2 factorise first ((2cos²x-1)²)^1/2this becomes (2cos²x-1)which equals cos 2xthe integral...