Integration of Functions of Several Variables
Integration of Functions of Several Variables MATH 2232 Multi Variable Calculus
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This 1 page Bundle was uploaded by Andrew Swann on Tuesday March 24, 2015. The Bundle belongs to MATH 2232 Multi Variable Calculus at George Washington University taught by Ullman in Spring2015. Since its upload, it has received 60 views.
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Date Created: 03/24/15
0 Integration of Functions of Several Variables Calc one reminder integral from a to b of fX length of ab X the average value of fab avg value has to do With integration Double Integrals Notation 2 integral signs fXy dA Where underneath the integral signs lies a capital R that stands for the region in the X y plane double integral of f over Rquot Interpretation Where the double integral equals the volume of a solid bounded in X y and the top is level With the plane or curved Where can just be the volume if everything is in positive Z axis but can be top bottom if Z intersects xy plane Assigned volume the double integral the area of R X the average value of f on R De nition limit of the towers you can draw from the xy plane up to the point on the z axis Computation Fubini s Theorem If its a rectangle R X y altXltb Cltyltd the double integral equals the integral from ab of the integral from czd of fXy dy dX can be done With the inside on the outside or vis versa Integration is additivehomogeneousand monotone additive if the integrand is fXy gXy you can separate the integral and add them homogeneous if you have a constant inside the integral signs the C can be pulled out monotone if fXy lt gXy for all values of Xy then the double int of f lt double int of g
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