What is the complete problem statement? You need to have some finite region in the plane to start with.togo said:Homework Statement
Given the following curve:
y = x^3
Use shell method and rotate around x-axis to determine the volume
togo said:Homework Equations
2pixy
The Attempt at a Solution
x(x^3) = x^4
Integrate
x^4 = 1/5 x^5
1/5(8)^5 = 6553.6
*2 = 13107.2 pi
the answer should be 768/7 pi, where did I go wrong? thanks.
For starters, if you are supposed to use shell method, revolving around the x-axis, than the integrand needs to be in terms of y, not x.togo said:the answer should be 768/7 pi, where did I go wrong? thanks.
As eumyang notes, you've used the disc method, not the shell method, but it still should produce the right answer. Your answer is wrong because you've calculated the wrong region. It is not bounded by y=0, it's bounded by y=8. Draw the bounded region in the XY plane.togo said:where did I go wrong? .
The curve shell method is a technique used to calculate the volume of a three-dimensional shape that is formed by rotating a curve around an axis. It differs from other methods, such as the disk or washer method, in that it uses cylindrical shells instead of discs or washers to approximate the shape.
The steps for using the curve shell method are as follows:
The curve shell method should be used when the shape being rotated has a varying cross-sectional area, as it is difficult to calculate the volume using other methods in this scenario. It is also useful for finding the volume of shapes that cannot be easily divided into simpler geometric shapes.
Some common mistakes to avoid when using the curve shell method include:
Yes, the curve shell method can be used for any type of curve as long as it can be rotated around an axis to form a three-dimensional shape. This includes curves such as parabolas, circles, and hyperbolas.