Question

Did I do this wrong? (revolving curve around a line)...

Answer 1

\[V= \pi \int\limits_{0}^{4} (3-\sqrt{x})^2 dx+ \int\limits_{4}^{6} (3-(6-x))^2 dx\]
and
\[V= \pi \int\limits_{0}^{4} (\sqrt{x}+2)^2 dx+ \int\limits_{4}^{6} ((6-x)+2)^2 dx\]

Answer 2

i'll draw the graph now.

Answer 3

What are the functions you started with..?

Answer 4

y=√x and y=6-x

I have to revolve around y=3 and y=-2.

Answer 5

they intersect at (4,2)

Answer 6

Regarding "Did I do this wrong? (revolving curve around a line)..." :

I see two different functions (each of which has its own "curve"). Would you mind choosing one of those functions so that we could concentrate on a simpler example? And would you mind if were were to revolve the region defined by that one function around the x-axis first, also as an example? Or shall we just jump in and solve the problem you've posted?

Answer 7

Sorry, they're two curves in one graph...
Alright, we can focus on revolving y=√x around y=3 and then y=6-x around y=3.

Answer 8

OK, then. Please consider the 3 different methods available to you and then choose one of them: disks, washers, shells.

Answer 9

shell

Answer 10

that's a good choice here. Would your shells be horiz or vertical?

Answer 11

i think horizontal .

Answer 12

Yes, because your axis of revolution is horiz. Nice work. How thick will each shell be? How would you represent the right-hand x-value of a given shell? the left-hand one? (Hint: You'll have to re-write y=Sqrt(x) and y=6-x.)

Answer 13

i'm sorry, can you tell me exactly what a shell would be? when i revolve, i look at it as a cylinder...

Answer 14

Yes, exactly; a shell is a hollow cylinder. In your first math problem the axis of this shell/cylinder will be the line y=3.

Have you used the Draw feature before? That'd be one way to show me what you have in mind.

Hint: the graph of y=Sqrt(x) defines the lower end of each shell (left end); thegraph of y=6-x defines the upper end (right end).

Willing to draw a diagram and to share it with me ?

Answer 15

i'm not sure. :( i haven't done a problem like this before. I've only done these with curves that intersect at a and b.

Answer 16

I'm going to sketch a graph of the 2 functions as quickly as possible. Then i'd like for you
to show me where they intersect, and to draw in one sample shell.