Quiz 11 - Math 53: Multivariable Calculus November 28, 2007...

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Unformatted text preview: Math 53: Multivariable Calculus November 28, 2007 Quiz 11 Lecturer: Prof. Michael Hutchings GSI: Gary Sivek Name: Answers 1. (6 pts) Evaluate contintegraltext C F d r , where F = 2 y + sin x 1 + x 2 i + x + e y 1 + y 2 j and C is the square with vertices (0 , 0) , (1 , 0) , (1 , 1) , (0 , 1). This would be rather difficult to do directly. But by Greens Theorem: contintegraldisplay C F d r = integraldisplayintegraldisplay bracketleftbigg x parenleftbigg x + e y 1 + y 2 parenrightbigg y parenleftbigg 2 y + sin x 1 + x 2 parenrightbiggbracketrightbigg dA = integraldisplay 1 integraldisplay 1 parenleftbigg 1 1 + y 2 2 1 + x 2 parenrightbigg dy dx = integraldisplay 1 bracketleftbigg tan 1 y 2 y 1 + x 2 bracketrightbigg 1 dx = integraldisplay 1 parenleftbigg 4 2 1 + x 2 parenrightbigg dx = 4 x 2tan 1 x vextendsingle vextendsingle vextendsingle 1 = 4 2 4 = 4 ....
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Quiz 11 - Math 53: Multivariable Calculus November 28, 2007...

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