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 ∫x² ln(4x)dx

Firstly , identify this question as integration by parts. Therefore set one half as value 'u' and one as value 'dv'.

Here we will set u = ln(4x).

Therefore: d...

*The usual mistake with inequalities is not with a students algebra, but with lack of consideration of the inequality signs. During a tutorial I would show their false method and my correct one and also s...

Use the product rule:

d/dx(fg) = f'g + fg'

f = x²    f' = 2x   g = sin(x)  g' = cos(x)

answer = 2xsin(x) + x²cos(x)

As the tangent has the same gradient as the curve at the particular point, we need to find the gradient of the curve. To find the gradient we need to differentiate. Due to there being two variables in thi...

Firstly, note that a stationary point can either be a local maximum, local minimum or point of inflexion. Now suppose you have a differentiable function (a graph which has a unique gradient/derivative at ...