Problem Statement
The problem for examination is evaluation of an integral of the form
where D is some two-dimensional area in the xy–plane. For some functions f straightforward integration is feasible, but where that is not true, the integral can sometimes be reduced to simpler form by changing the order of integration. The difficulty with this interchange is determining the change in description of the domain D.
The method also is applicable to multiple integrals.
Sometimes, even though a full evaluation is difficult, or perhaps requires a numerical integration, a double integral can be reduced to a single integration, as illustrated next. Reduction to a single integration makes a numerical evaluation much easier and more efficient.
Read more about this topic: Order Of Integration (calculus)
Famous quotes containing the words problem and/or statement:
“The disesteem into which moralists have fallen is due at bottom to their failure to see that in an age like this one the function of the moralist is not to exhort men to be good but to elucidate what the good is. The problem of sanctions is secondary.”
—Walter Lippmann (1889–1974)
“Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.”
—Charles Sanders Peirce (1839–1914)