Homework5Solns

Homework5Solns - SHORT CALCULUS Math 16C Sec 2 Spring 2008...

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Unformatted text preview: SHORT CALCULUS Math 16C Sec 2 Spring 2008 Homework #5 Solutions Peter Malkin Section 7.9 Question 4 The region of integration is R = { ( x, y ) : 0 y 6 , y 2 x 3 } . integraldisplay 6 integraldisplay 3 y 2 ( x + y ) dxdy = integraldisplay 6 bracketleftbigg 1 2 x 2 + xy bracketrightbigg 3 y 2 = integraldisplay 6 parenleftbigg 1 2 3 2 + 3 y- 1 2 parenleftBig y 2 parenrightBig 2- y 2 y parenrightbigg dy = integraldisplay 6 parenleftbigg 9 2 + 3 y- 5 8 y 2 parenrightbigg dy = bracketleftbigg 9 2 y + 3 2 y 2- 5 24 y 3 bracketrightbigg 6 = (27 + 54- 45)- (0) = 36 Question 18 The region of integration is R = { ( x, y ) : 0 x 2 , y x } = { ( x, y ) : 0 y 2 , y x 2 } . The volume of the specified solid is V = integraldisplay 2 integraldisplay x 6 dydx = integraldisplay 2 [6 y ] x = integraldisplay 2 6 xdx = bracketleftbig 3 x 2 bracketrightbig 2 = 12 1 or V = integraldisplay 2 integraldisplay 2 y 6 dxdy = integraldisplay 2 [6 x ] 2 y dy = integraldisplay 2 (12- 6 y ) dy = bracketleftbig 12 y- 3 y 2 bracketrightbig 2 = (24- 12)- (0) = 12 . Question 24 The region of integration is R = { ( x, y ) : 0 x, y } ....
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Homework5Solns - SHORT CALCULUS Math 16C Sec 2 Spring 2008...

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