Question

the functions f and g are given f=sqrt(x) and g = 6-x. Let R be the region bounded by the x-axis and the graphs of f and g. Find the area of R

Answer 1

can someone help

Answer 2

first step is to get an idea of the shape of the area:it looks like we will have to do two separate integrals, because we can see that before the line x=xo we have the area as g-f, and after given by f-g.
xo occurs when the functions intersect, so we can find it by solving\[f(x)=g(x)\]for x.
our integral to find R will then be\[R=\int_{0}^{x_o}g-fdx+\int_{x_o}^{6}f-gdx\]