Let R be the region that lies between the curves y=x^m and y=x^n, 0≤x≤1, where m and n are integers with 0≤n

Question

Let R be the region that lies between the curves y=x^m and y=x^n, 0≤x≤1, where m and n are integers with 0≤n<m.
a)sketch the region R
b)Find the coordinates of the centroid of R
c)Try to find values of m and n such that the centroid lies outside R

perl · Answer

so two quadratic curves

miracrown · Answer

http://prntscr.com/50v471

miracrown · Answer

It will help at the start to make a rough sketch of the region R between these 2 curves.
Even though n and m are arbitrary integers, let’s make a sketch for the case that n = 2 and m = 3.

miracrown · Answer

http://prntscr.com/50v4mq Notice that the higher integer curve (m in our case) lies below the lower integer curve (n) The region R is the crescent between these 2 curves.

ganeshie8 · Answer

$$\large   x\in(0,1) \&\& n\gt m \implies   x^n \lt  x^m  $$

ganeshie8 · Answer

this is going to be a very interesting(challenging) problem i guess

perl · Answer

xbar = integral  / integral

dan815 · Answer

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