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We can think of taking the logarithm base a of a number b (log_ab) as "the number of times we need to multiply a by itself to get b". So for example, log₂ 16 = 4, since we n...

This problem can be solved by squaring both sides of the inequality, as this removes the modulus from the problem. Modulus or | | means that a term can take positive and negative values, which could also ...

In order to differentiate something like y=3xsinx, you need to make use of the product rule. The product rule says that when you have an equation in the form y=f(x)g(x), you can find y' by using the formu...

Firstly we need to find the stationary points, we know that when the first derivative of the curve is equal to 0, this means it is a stationary point as there is no effective gradient.
The first deri...

The area can be found using a definite integral.
Integral from 0 to 5 of [3x² ] = [x]⁵₀ = 5 - 0 = 5