Bachelier said:Can the Surface area of a revolution be NEGATIVE? I am calculating this in parametric equations?
finally I hope this is the right forum to ask this question.
The formula for finding the area of a surface of revolution around the x-axis is A=2π∫(x)(f(x))dx, where x is the variable of integration and f(x) is the function representing the curve.
Yes, this formula can be used for any shape as long as the curve is rotated around the x-axis to create a solid shape.
This formula is derived from the concept of calculus known as the "disk method", where the surface of revolution is divided into infinitely thin disks whose areas can be calculated using the formula for the area of a circle. The sum of all these areas gives us the total surface area of the shape.
The units of measurement for the surface area will depend on the units used for the function representing the curve. For example, if the function is in meters, then the surface area will be in square meters.
Yes, this formula can be extended to find the volume of a solid of revolution by simply integrating the function f(x) instead of multiplying it by x. The resulting formula would be V=π∫(f(x))^2dx.