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en bloc
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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 !en bloc said: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).
Yes, of course! I get that, but what did you mean byen bloc said: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
You need at least one more boundary; perhaps the x-axis ?en bloc said:it's the region bounded by y = [itex]\sqrt{}x[/itex] and x = 4
Assuming that the problem is:en bloc said: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).
The shell method is a technique used in calculus to find the volume of a solid of revolution. It involves integrating the area of a cylindrical shell that is created by rotating a function around a given axis.
The value of p(x) in the shell method depends on the shape of the solid and the axis of rotation. Generally, p(x) represents the distance from the axis of rotation to the edge of the cylindrical shell at a given point. It can be determined by setting up the integral and considering the cross-sections of the solid.
In the shell method, p(x) represents the distance from the axis of rotation to the edge of the cylindrical shell, while r represents the radius of the cylindrical shell. While they may seem similar, they are used in different contexts and have different values depending on the solid being rotated.
Yes, p(x) can be negative in the shell method. This can occur when the solid being rotated has portions that are below the axis of rotation. It is important to properly set up the integral and consider the negative values when determining the bounds of integration.
If p(x) is not constant in the shell method, the integral will need to be set up as a function of x or y (depending on the axis of rotation). This means that the bounds of integration will also be functions, and the integral will need to be evaluated using techniques such as u-substitution or integration by parts.