1. Feb 22, 2006

### nick727kcin

it gave me two figures and explained how they look, so i sketched them as they are. i dont have a problem with centroids, but i do with this particular problem.

this is the question:

Let R be the region that lies between the curves of y=X^m and y=x^n.
0=<x=<1
(0 is less than or equal to x, which is less tahn or euqal to 1)

0=<n<m
a) sketch the graph (already done)
b) find the coordinates of the centroid of R

2. Feb 22, 2006

### nick727kcin

also what would R be? would it be x^n-x^m

3. Feb 22, 2006

### quasar987

Have you ever heard something to the avail of "$\int_a^b f(x)dx$ is the area under the curve f(x) from a to b"?

4. Feb 22, 2006

### nick727kcin

youre right, but where would the object be?

5. Feb 22, 2006

### nick727kcin

would the object take form in the shaded region?

6. Feb 22, 2006

### HallsofIvy

Staff Emeritus
There is no shaded region! Also it makes no sense to say "Would R be x^n-x^m?" because R is a region not a function. Okay, you have drawn the graphs. You are looking for the centriod of the region between the two graphs and between x= 0 and x= 1. Integrate xm- xn (assuming m> n) between 0 and 1.