L24 Math 233 Lecture 26: L24 Math 233 Lecture 26- Iterated Integrals
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Double integrals: d b a c (x, ) y is the function and. [a,b]x[c,d] is the rectangle r in which f is defined is the area of element dxdy. Method 1 (x first): yda x2 on r = [0,3]x[1,2] Limits on integrals refer to its variable (fubini) Theorem: if f(x,y) is continous on r = [a,b]x[c,d] then d b c a (fubini"s theorem) (x, )dydx (x, )dxdy (x, )da d c b a b a d c y y y f f f. Use this theorem to simplify complicated double integrals. Based on fubini"s theorem, we can choose y first and avoid doing integration by parts x s. Note: must assert fubini"s theorem to to this iterated integral in this way. Thus, you must mention that the function is continuous in the rectangle given. Find the volume under planes. x2 + 2 2 + z = 1 y. 6 bounded by x=2, y=2, and the 3 coordinate.
