Recognize when a function of three variables is integrable over a closed and bounded region. Evaluate a triple integral by expressing it as an iterated integral. In3(b), we found r u r v h ucosv usinv ui. Learning Objectives Recognize when a function of three variables is integrable over a rectangular box. the parameter domain of the parameterization is the set of points in the uv -plane that can be substituted into r. ux integral is ZZ S 1 FdS ZZ R F(r(u v)) (r u r v) dA: To nd F(r(u v)), we just plug our parameterization into F(x y z) h0 0 zi, which gives F(r(u v)) h0 0 ui.
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