Originally Posted by

**esbo**
Originally Posted by

**Arcane_Mathamatition**
Originally Posted by

**esbo**
Prove the integral of x cubed is x to the forth divided by 4 for example.

using the limit of riemann sums would give you the proof quite nicely.

OK use tthat if you must, please post you solution asap, preferebaly this year or whenever you have completed it

alright, no problem. Assuming you will agree that the best way to approximate the area under a curve is to 'carve' it up into a bunch of rectangles, then the smaller the width of each rectangle, the more accurate the approximation is, correct? going on that, we have a sum,

and this is going to equal the added area of all of our rectangles if we start at some point, 'a' and take the area up until some other point 'b'. so, taking right end-points on our graph, we will get area's such that

such that the area of any given rectangle, is the change in x, multiplied by the function evaluated at it's right end point. So,

yes? Now, the only problem I currently have is that this only applies to a rectangle, but it clearly shows how, when the difference between the points goes to zero, the total area will be a function of one order higher, which is also obvious if you consider the are to be the 'height' (y) times the 'width' (x). That is to say, when

, it should be obvious that the area function will be some function of

The problem being finding the constant that will give you the proper area. If anyone would like to give me a push in the right direction here, by all means