Integrate the following between 0 and 1: (x + 2)^3 dx

Initially, we must recognise the simplest way to integrate this equation is using the 'reverse chain rule' method. 

This means raising the value of the power, in this case '3', by one, and then dividing by the new value of the power (which is four). This gives the integral to be 1/4 * (x + 2)^4 + c where c is a constant. We can check that this is correct by differentiating to give the original equation.

This is a definite integral, as there are bounds, so we must evaluate this new equation between 1 and 0: 

[1/4 * (x + 2)^4 + c] between 1 and 0 gives: 1/4[((1+2)^4 + c) - ((0 + 2)^4 + c)] = 1/4[81 - 16] = 16.25