The advantage of the Fubini Tonelli over Fubini's theorem is that the repeated integrals of the absolute value of | " f " | may be easier to study than the double integral.
22.
If the double integral exists, then it is equal to each of the two iterated integrals ( either " " or " " ) and one often computes it by computing either of the iterated integrals.
23.
Although this formula provides a closed expression for the surface area, for all but very special surfaces this results in a complicated double integral, which is typically evaluated using a computer algebra system or approximated numerically.
24.
It's not hard to check that | f ( x, y ) | is not integrable, and that the double integrals are different . talk ) 06 : 07, 11 March 2008 ( UTC)
25.
With double integrals, we are trying to find a volume under a curve, within a rectangle R . We have dA, which is the product of dx and dy, and a height z, which varies with dx and dy.
26.
Notice that, by convention, the double integral has two integral signs, and the triple integral has three; this is a notational convention which is convenient when computing a multiple integral as an iterated integral, as shown later in this article.
27.
The integration by substitution article states this in terms of measure theory, but I'm sure the proof for this can't be that much more complicated than the case of double integrals .-- ( talk ) 00 : 20, 13 June 2013 ( UTC)
28.
In physics and mathematics, "'Green's theorem "'gives the relationship between a line integral around a simple closed curve " C " and a double integral over the plane region " D " bounded by " C ".
29.
Separating the " A " and " B " terms, the right hand side can be written as a double integral starting in the " x " or " y " direction, to which the fundamental theorem of calculus can be applied.
30.
Green's Theorem, which gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C, is applied in an instrument known as a planimeter, which is used to calculate the area of a flat surface on a drawing.
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