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# sn13_1 - Math 2433 Week 13 Notes Popper013 1"Shambala(or...

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Math 2433 Week 13 Notes Popper013 1. "Shambala (or Shambhala)", a mythical Buddhist city said to be located somewhere in the Himalayas, is the subject of a song recorded by which of the following bands? A. The Doors B. Credence Clearwater Revival C. Three Dog Night D. Jefferson Airplane 17.1 Line Integrals and Work Given 1 2 3 ( , , ) ( , , ) ( , , ) ( , , ) x y z h x y z h x y z h x y z = + + h i j k , a vector function (vector field) defined on some region Ω in space, and a smooth curve (or piecewise smooth curve) C : ( ) ( ) ( ) ( ) , u x u y u z u a u b = + r i+ j k in Ω Or given 1 2 ( , ) ( , ) ( , ) x y h x y h x y = + h i j , a vector function (vector field) defined on some region Ω in the plane, and a smooth curve (or piecewise smooth curve) C : ( ) ( ) ( ) , u x u u a u b = r i+y j in Ω The line integral of h over the curve C , denoted by ( ) C h r dr is the number given by: ( ) [ ( )] ( ) b C a u u du = h r dr h r r

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Examples 1. Set ( , , ) x y z xy yz xz = + + h i j k and let C be the curve: 2 3 ( ) , 0 2 u u u u u = + r i+ j k Find ( ) C h r dr 2. Set ( ) ( ) ( , ) 2 2 x y xy y x y = + + + h i j , find ( ) C h r dr on: a) C 1 : The parabola 2 y x = from (1,1) to (3,9)
b) C 2 : The line segment from (1,1) to (3,9) ***NOTE: The value of the line integral of h depends upon the path; different paths give different values.

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