hvidales said:Homework Statement
The curve x=y^(2) and the line x=4 is rotated about the x axis.
Homework Equations
pi* integral from a to b of Radius^(2)
The Attempt at a Solution
pi* integral from 0 to 4 of (square root of x)^(2) dx.
My teacher has this answer as 8pi but I think that that is wrong. Shouldn't it be 16 pi because you have to account for symmetry?
hvidales said:I see! How would you do this if you are doing the shell method? I am stuck at this part:
2pi* integral from -2 to 2 of y[4-y^(2)] dy. I am stuck there lol.
The purpose of rotating a curve and line around the x-axis is to create a three-dimensional representation of the two-dimensional curve and line. This allows for a better understanding of the shape and its relationship to other objects in space.
The steps involved in rotating a curve and line around the x-axis include finding the coordinates of the points on the curve and line, determining the angle of rotation, using trigonometric functions to calculate the new coordinates after rotation, and plotting the new points to create the rotated shape.
The angle of rotation determines the amount of rotation that will occur. A larger angle will result in a more significant change in the shape, while a smaller angle will result in a smaller change. The direction of rotation (clockwise or counterclockwise) is also determined by the angle of rotation.
Rotating a curve around the x-axis involves rotating each individual point on the curve, while rotating a line involves rotating the entire line as a single object. Additionally, the resulting shape of a rotated curve will generally be curved, while a rotated line will remain straight.
Yes, there are many real-world applications of rotating a curve and line around the x-axis. For example, it is used in computer graphics to create three-dimensional images, in engineering to design complex structures, and in physics to study the motion of objects in space.