A curve has the equation y=3x^3 - 7x^2+52. Find the area under the curve between x=2 and the y-axis.

With a question like this. Firstly you have to read it, of course. But more importantly you have to understand what it is asking of you. So it is asking to find the area with boundaries at x=2 and the y axis which is x=0 and under the curve. Then when we think well what do I do? Well I can integrate but is there something more than I need to do beforehand, do I need to find where the curve crosses the coordinate axes? So we can see that we don't need to find the coordinate axes. We can just integrate the equation by raising the variable x of each term by a power of 1 and then divide the coefficient of that term by the new power which is the original power plus one. If the term is a constant, just a number, then the integral would be that constant times by x. Reason being, before integration, x had a power of zero, so to integrate we add a power on the x term so it'd become x which is the same as x to the power of 1. Afterwards substitute limit of 1 into the equation and then subtract the equation when 0 is substituted into it. Then tidy the answer and you've got your answer!