2224-Sec13_2-HWT

2224-Sec13_2-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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Math 2224 Multivariable Calculus – Sec. 13.2: Double Integrals over General Regions I. Types of Regions We will be discussing two types of general regions in this section A. Type I An xy -region on the xy -plane is called a type I region if any vertical strip (in the y direction) always has the same upper and lower boundaries and the set can be described by the set of inequalities a ! x ! b , g 1 ( x ) ! y ! g 2 ( x ) . B. Type II An xy -region on the xy -plane is called a type II region if any horizontal strip (in the x direction) always has the same right and left boundaries and the set can be described by the set of inequalities c ! y ! d , h 1 ( y ) ! x ! h 2 ( y ) . C. Type I Type II both types II. Fubini’s Theorem (Stronger Form) Let f(x,y) be continuous on a region R. 1. If R is defined by a ! x ! b , g 1 ( x ) ! y ! g 2 ( x ), with g 1 ( x ) and g 2 ( x ) continuous on [ a,b ], then f ( x , y ) dA R !!
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2224-Sec13_2-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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