Question

Find the centroid of the thin plate bounded by the graphs of the functions g(x)=x^2 and f(x)=x+6 and M=area of the region covered by the plate.

Answer 1

\[\frac{M_y}{M},\frac{M_x}{M}\]

Answer 2

\[\left\{\frac{\int _{-2}^3\int _{x^2}^{(x+6)}xdydx}{\int _{-2}^3\int_{x^2}^{(x+6)} dy \, dx},\frac{\int _{-2}^3\int _{x^2}^{(x+6)}ydydx}{\int _{-2}^3\int_{x^2}^{(x+6)} dy \, dx}\right\}\]

Answer 3

{1/2, 4}

Answer 4

this is the center point of your region