- #1
HallsofIvy said:If you can't be bothered to
1) type the problem itself here
2) Do anything at all at all on the problem
I don't see why I should bother.
tiny-tim said:Hi abcdefg10645! That's better!
(have a del: ∇ and a dot: · and an integral: ∫ )
For 1, make the obvious substitution …
u = 3x + y, v = x - 2y, dxdy = … ?
For 2, just write each of the coordinates out in full …
try a. first …
what do you get?
abcdefg10645 said:Could you give me a hint for changing the upper and lower limit?
A double integral can be thought of as a mathematical tool used to calculate the volume under a surface in two-dimensional space. It involves evaluating the function at different points within a given region and summing up these values.
Vector calculus involves the study of vector fields and their properties. Double integrals are used in vector calculus to calculate flux, which is the amount of fluid, energy, or particles that pass through a given surface. This is an important concept in understanding how vector fields behave.
There are two types of double integrals: iterated integrals and double integrals over a region. Iterated integrals involve integrating a function with respect to one variable at a time, while double integrals over a region involve integrating a function over a two-dimensional region in one step.
To set up a double integral, you first need to determine the limits of integration, which are the boundaries of the region over which the integral will be evaluated. Then, you need to choose the order of integration, which is the order in which the variables will be integrated. Finally, you need to write the function to be integrated in terms of the chosen variables and set up the integral using the appropriate notation.
Double integrals and vector calculus have various applications in physics, engineering, and economics. They can be used to calculate the work done by a force, the flow of a fluid, the area of a surface, and the volume of a solid. They are also essential in understanding and solving problems related to electric and magnetic fields, fluid dynamics, and optimization.