The functions f and g are given by f(x)=sqrt(x) and g(x)= 6-x. Let R be the region bounded by the x-axis and the graphs of f and g.
a) Find the area of R.
b) The region R is the base of a solid. For each y, where 0

Question

The functions f and g are given by f(x)=sqrt(x) and g(x)= 6-x. Let R be the region bounded by the x-axis and the graphs of f and g.
a) Find the area of R.
b) The region R is the base of a solid. For each y, where 0<y<2, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 2y. Write, but do not evaluate, an integral expression that gives the volume of the solid.
c) There is a point P on the graph of f at which the line tangent to the graph of f is perpendicular to the graph of g. Find the coordinates of point P.

turingtest · Answer

step 1)
find the intersection of the graphs f and g

anonymous · Answer

it's 4,2 it's given on the figure

turingtest · Answer

|dw:1330661449878:dw|the first part of the area is under f(x) from x=0 to x=4
the next part is the area under g(x) from x=4 to x=6
so you need two integrals for the area
got that yet?