)myfunkymaths said:
tiny-tim said:hi myfunkymaths!
(have a square-root: √ and try using the X2 icon just above the Reply box
uhh? isn't that just integrating r - 5 over the sphere r = 3 ?
Double integrals are mathematical tools used to calculate the area under a surface in two dimensions. They are an extension of single integrals, which are used to calculate the area under a curve in one dimension.
To solve a double integral, you need to first set up the limits of integration for both the inner and outer integrals. Then, you evaluate the inner integral first, treating the outer integral as a constant. Finally, you integrate the result of the inner integral to solve the outer integral.
There are two types of double integrals: iterated integrals and double integrals over general regions. Iterated integrals are used when the limits of integration are constant values, while double integrals over general regions are used when the limits of integration are functions.
Double integrals are useful in many scientific and mathematical fields, including physics, engineering, and economics. They allow us to calculate the volume, mass, and other properties of objects and surfaces in two dimensions.
Some common mistakes when solving double integrals include incorrectly setting up the limits of integration, forgetting to evaluate the inner integral first, and mixing up the order of integration. It is important to carefully check the limits and order of integration to avoid these errors.