Fall 2007 - Hohnhold's Class - Quiz 2 (Version A)

# Fall 2007 - Hohnhold's Class - Quiz 2 (Version A) - x and...

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Quiz 2 for Math 20B Fall Quarter 2007, UCSD Henning Hohnhold Name: Section: #1: #2: Total: (1) (5 points) Please sketch the region enclosed by the curves x - y 2 + 2 y = 0 and x + y = 2 and compute its area. The sketch looks like this: -2.4 -1.6 -0.8 0 0.8 1.6 2.4 3.2 4 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 The area is given by Z 2 - 1 2 - y - ( y 2 - 2 y ) dy = 9 2

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(2) (5 points) Sketch the ellipse given by the equation x 2 + 1 4 y 2 = 1 . (Hint: Find the intersection points with the
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Unformatted text preview: x- and y-axes ﬁrst.) Compute the volume of the solid obtained by revolving the ellipse around the y-axis.-2-1.6-1.2-0.8-0.4 0.4 0.8 1.2 1.6 2-2-1.5-1-0.5 0.5 1 1.5 2 The resulting volume is given by π Z 2-2 r 1-( y 2 ) 2 2 dy = π Z 2-2 1-( y 2 ) 2 dy = 8 3 π 2 Good Luck! 3...
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Fall 2007 - Hohnhold's Class - Quiz 2 (Version A) - x and...

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