FinalReview4 - with vertices (0,0), (3,0), and (1,2). Find...

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\ \ 54. DO. Jt. Math 1710 Final Review 1 The region between the graphs of y - 12 62. and y: * + |r2 is revolved about the gr- axis to form a lens. Compute the volume of the lens. Find the volume of the solid formed by revolving the region enclosed by the graph of r2/3 +a2/3 _ a2/3 about the z-axis. Find the volume of the solid obtained by rotating the area in the plane bounded by a : sin(r2), the z-axis, r : o and /- ': :x : | 7r l'z aDout lne E-axls. Find the center of mass of a wire that ex- tend along the number line from 0 to 4 and whose cross section area when sliced perpendicular to the number line is a cir- cle with radius 0.0012 + 0.1.
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Unformatted text preview: with vertices (0,0), (3,0), and (1,2). Find the center of mass of the region in the plane bounded by A : r - 3 and *: (a + 3)(E - t). Find the center of mass of the planar re-gion bounded by a : 12 and g : tr3. Now do the same thing with y : rn and U : trn*r. Is the center of mass of a con-nected planar object always inside the obiect? 61. State the first form of the Fundamental Theorem of Calcuius. Prove it. 4 . .?r.i {!tr- I l State the second form of the Fundamen-tal Theorem of Calculus. Prove it. (You may use the first form in your proof.) 58. 59. 60....
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This note was uploaded on 10/22/2010 for the course MATH MATH 1710 taught by Professor Brand during the Fall '07 term at North Texas.

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