Question

The functions f and g are given by f(x)=√x and g(x)=6-x. Let R be the region bounded by the x-axis and the graphs of f and g, as shown in the figure in the link below. Please show your work.

Answer 1

The functions f and g are given by f(x)=√x and g(x)=6-x. Let R be the region bounded by the x-axis and the graphs of f and g, as shown in the figure in the link below. Please show your work.

http://goo.gl/jXIZD

1. Find the area of R.
2. 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.
3. 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.

Answer 2

I calculated 22/3 for 1. Is that right? What do I do for 2 and 3?

Answer 3

@hartnn @experimentX

Answer 4

wow .. could you summarize ... I am hard time reading through all.

Answer 5

one by one.

Answer 6

hmm
for area of region you can do
\[ \int_0^4 f(x) dx + \int_4^6 g(x) dx\]

Answer 7

Right. I believe I've already gotten the answer for the area. Which is exactly what you gave. Which ends up being 16/3 + 2 = 22/3. I'm not sure what to do for 2 and 3.

Answer 8

could you draw figure of 2 ??

Answer 9

Is that what it's supposed to look like? It says the height is 2y and the base is R (which I don't understand).