Jbreezy said:Homework Statement
I want the surface area of Revolution about x from [-2,2] of y = |x|
So I want to know if I can take it x from [0,2] and just multiply this result by 2?
Homework Equations
The Attempt at a Solution
Set up
dy/dx = (5/(2√x))
S = 2 ∏ ∫ 5x^1/2(√ 1 +((5/(2√x))^2)
from x = 0 , to x = 2. Then multiply this result by 2? Is this OK to do?
The surface area of revolution refers to the total area of a three-dimensional figure obtained by rotating a two-dimensional shape around a given axis. This is often used in mathematics and engineering to calculate the surface area of objects such as cones, cylinders, and spheres.
The surface area of revolution can be calculated using integral calculus. The formula for calculating the surface area of revolution is 2π∫f(x)√(1+(f'(x))^2)dx, where f(x) is the function defining the shape of the rotated figure and f'(x) is its derivative.
The surface area of revolution has many real-world applications, such as in architecture for calculating the surface area of domes and arches, in manufacturing for determining the amount of material needed to create a curved surface, and in physics for calculating the surface area of objects in motion.
The shape of the original two-dimensional figure has a direct impact on the surface area of revolution. For example, a cylinder with a larger base will have a larger surface area of revolution than one with a smaller base. This is because the shape of the two-dimensional figure determines the curvature and dimensions of the three-dimensional figure.
One limitation when calculating the surface area of revolution is that it can only be applied to objects with rotational symmetry. This means that the shape of the object must be able to be rotated around a given axis without changing. Additionally, the integration required for the calculation can be complex and time-consuming for more intricate shapes.