Unformatted text preview: 62.5 pounds.) Do not evaluate the integral. 2. (a)(20 points) ±ind the volume V of the solid whose base is a circle of radius 2, such that the cross sections of the solid perpendicular to a Fxed diameter of the base are squares. (b) (20 points) Let S be the region bounded between the curves y = x 2 and y = 1. The area of S is 4/3. Compute ( x, y ), the center of gravity of S . 3. (25 points) ±ind the length L of the curve described parametrically by ( x,y ) = ( e-t cos( t ) ,e-t sin( t )) , ≤ t < π . 4. Suppose z = 1 + i √ 3. (a) (3 points) What is | z | ? (b) (3 points) ±ind real numbers a,b such that a + ib = 1 /z . (c) (4 points) ±ind real numbers R,θ such that z = Re iθ ....
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- Fall '08
- Math, TA, cylindrical water tank