What p(x) should be in shell method

[en bloc]

Homework Statement

y=x^(1/2) x=4

find volume of revolution about the line x=4

this was a test problem and i chose x as p(x) [radius] but now i think that it should've been (x+4).

 

[SammyS]

Homework Statement

y=x^(1/2) x=4

find volume of revolution about the line x=4

this was a test problem and i chose x as p(x) [radius] but now i think that it should've been (x+4).

I'm confused too !

What question are you asking?

 

[en bloc]

In calculus II, graphing a function and then revolving it around an axis. calculate that volume either by disk/washer method or shell method.

and the formula for the shell method is 2\pi \int_{a}^{b} (p(y)h(y))\,dy

 

[SammyS]

In calculus II, graphing a function and then revolving it around an axis. calculate that volume either by disk/washer method or shell method.

and the formula for the shell method is

2\pi \int_{a}^{b} (p(y)h(y))\,dy

Yes, of course! I get that, but what did you mean by

y=x^(1/2) x=4​

I'd rather not have to guess when I'm answering someones question.

 

[en bloc]

it's the region bounded by y = \sqrt{}x and x = 4

 

[SammyS]

it's the region bounded by y = \sqrt{}x and x = 4

You need at least one more boundary; perhaps the x-axis ?

 

[en bloc]

i thought the same thing, y = 0, but it wasn't given. part (a) of the problem was revolution around the x-axis. i just implicitly assumed it was. so what would p(x) be in this region.

 

[SammyS]

Homework Statement

y=x^(1/2) x=4

find volume of revolution about the line x=4

this was a test problem and i chose x as p(x) [radius] but now i think that it should've been (x+4).

Assuming that the problem is:

Find the volume of revolution, using the shell method, if the region bounded by y=x^1/2, x=4, and y=0 is revolved about the line x = 4.​

The radius is the distance that an arbitrary value of x is from x=4. That distance is |x-4|. Assuming that the integration is done
from x = 0 to x = 4, then, |x-4| = 4 - x .