Noone1982 said:"Find the surface integral of r over a surface of a sphere of radius and center at the origin. Also find the volume integral of Gradient•R and compare your results"
Do I just integrate r to get (1/2)r^2 and plug some limits in since the r-hats equal one?
A surface integral is a mathematical concept used in calculus to calculate the amount of a function over a given surface. It is similar to a regular integral, but instead of integrating over a one-dimensional curve, it integrates over a two-dimensional surface.
To set up a surface integral, you first need to define the surface in terms of a parametric equation or as a graph of a function. Then, you can use a double integral to integrate the function over the surface.
Surface integrals have various applications in physics, engineering, and other fields. They are used to calculate the flux of a vector field through a surface, the surface area of a curved object, and the work done by a force on a surface.
The main difference between a surface integral and a line integral is the dimensionality of the object being integrated over. A line integral integrates over a one-dimensional curve, while a surface integral integrates over a two-dimensional surface.
Evaluating a surface integral involves finding the limits of integration for both the inner and outer integral and then solving the integral using techniques such as u-substitution or integration by parts. It is important to carefully set up the integral and use the correct limits for an accurate evaluation.