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You will end up with an equation with the form y = mx + c you should be familiar with from GCSE First you would need to differentiate the equation of the line For example if you had f(x) = x 3 + 2x and the c...

Curve: y = 3x 2 (x+2) 6 Coordinate: (-1, 3) This is typically a C3/4 level question because of the differentiation, but the rest of the question is possible with year 12 maths knowledge. The best way to tack...

Use substitution u=cos(x) resulting in du=-sin(x)dx: ∫ 0 π/2 sin(x)cos(x)^2dx = ∫ 0 π/2 -u^2du = [-1/3 u^3] x=0 x=π/2 = [-1/3 cos(x)^3] 0 π/2 = (-1/3 cos(π/2)^3) - (-1/3 cos(0)^3) = (-1/3 0^3 ) - (-1/3 1^3) ...

Recall that the derivative of exp(x) is exp(x), but notice this question is slightly more complex due to the x^2 term. This is example of differentiationg composite functions, and so the chain rule is requir...

We can understand this identity in two different, useful ways. Firstly, we can use Euler's identities from trigonometry to obtain the desired result using straightforward algebra. We know that: [1] sin(x) = ...