Find the centroid of the region bounded by the given curves. give your answers correct to two decimal places. y = x^3, x + y = 10, y = 0

The centroid is the point ()=(4.32,2.62)

Step-by-step explanation:

We graph the functions given in the attached picture. As you can see the region R is surrounded by the functions:

y=x³

y=10-x

y=0

This region can be divided by 2, where the first is delimited by y=x³ (0≤x≤2) and the second is y=10-x (2≤x≤10).

The centroid of region is given by:

First, we have to find the value of

=

=(16/4-0)+(100-50-20+2)=4+32=36

Now we find :

=

=

Then, we find :

=

=

Hence,

The centroid is the point ()=(4.32,2.62)

so, converting firstly the mixed fractions to improper fractions and then "adding".