Test3 - a rotated about the y axis. The center of the...

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Name MAC 3472, Honors Calculus 1 Keesling Test 3 12/8/09 Do all problems. Show your work and explain your answers. Each problem is 20 points. 1. Determine the following antiderivatives. Give the method used and explain the steps. (a) 1 4 ! x 2 dx " (b) sin 5 ( x ) dx ! 2. Determine the centroid of the area bounded by the x– axis, f ( x ) = x n , and the vertical line x = 2 .
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3. (a) Use Pappus’ Theorem to determine the volume of the torus below. The torus is the area of a circle of radius
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Unformatted text preview: a rotated about the y axis. The center of the circle is distance b from the y axis. (b) Use Pappus Theorem to determine the surface area of the torus in (a). 4. Do three iterations of Picard Iteration for the following differential equation. dx dt = t ! x 2 x (0) = 1 x ! 1 x 1 = x 2 = x 3 = b a x ! axis y ! axis 5. Solve the following differential equations. Show all steps. (a) dx dt = x ! t 2 (b) dx dt ! 4 x = e 2 t...
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This note was uploaded on 07/14/2011 for the course MAC 3472 taught by Professor Jury during the Spring '07 term at University of Florida.

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Test3 - a rotated about the y axis. The center of the...

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