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# multiple integral

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An integral involving two or more integrations with respect to different variables, where the integrations are carried out sequentially and variables other than the one being integrated with respect to are treated as constants. A double integral is the special case where two integrations are involved. Multiple integrals can be definite or indefinite. In the indefinite case, the first constant of integration will then integrate to be a function of the second variable etc. Where a surface is defined by a function z=f(x, y), the volume under the surface can be obtained by evaluating ∬f(x, y)dx dy. Strictly this should be written as {∫f(x, y)dx}dy but the brackets are usually omitted. For example, to find the volume under z=x+3y+5 in the ranges 0≤x≤2, 0≤y≤3 the required integral would be

Subjects: Mathematics.

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