In coordinates, these integrals become ( are defined as ) ordinary multiple integrals in . talk ) 13 : 39, 5 May 2014 ( UTC)
12.
"Because it is impossible to calculate the antiderivative of a function of more than one variable, indefinite multiple integrals do not exist so they are all definite integrals ."
13.
Since the concept of an antiderivative is only defined for functions of a single real variable, the usual definition of the indefinite integral does not immediately extend to the multiple integral.
14.
To denote multiple integrals, Newton used two small vertical bars or primes ( ), or a combination of previous symbols & ensp;, to denote the second time integral ( absity ).
15.
Smirnov's principal works in mathematical statistics and probability theory are devoted to the investigation of limit distributions by means of the asymptomatic behaviour of multiple integrals as the multiplicity is increased with limit.
16.
If the integral is not absolutely convergent, care is needed not to confuse the concepts of " multiple integral " and " iterated integral ", especially since the same notation is often used for either concept.
17.
:It may be best to think of the factors of \ cos \ alpha and \ cos \ theta as arising from the Jacobian to transform from Cartesian coordinates to spherical coordinates ( compare Multiple integral # Spherical _ coordinates ).
18.
My personal view is that once the dimension goes above 3, multiple integral signs would be obnoxious, and below 3 it's a matter of personal choice . talk ) 15 : 55, 7 November 2013 ( UTC)
19.
He is the author of several treatises, including one on the solution of numeric equations with multiple unknowns ( 1842 ); one on multiple integrals and their integrability conditions; and one on the determination of the orbits of the comets.
20.
In mathematics & mdash; in particular, in multivariable calculus & mdash; a "'volume integral "'refers to an integral over a 3-dimensional domain, that is, it is a special case of multiple integrals.
