Fin Ex REVIEW

# Fin Ex REVIEW - Final Exam Review Math 272 Stewart 1 Find...

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Math 272, Stewart 1. Find the arc length of the graph of y = 2x over the interval [0,1]. Show that the answer agrees with the formula for the distance between two points. 2. Find the area of the surface formed by revolving the graph of 3 ) ( x x f = on the interval [0,1] about the x axis. 3. A cylindrical water tank 12 feet high with radius of 8 ft is buried so that the top of the tank is 3 feet below ground level. How much work is done in pumping a full tank of water up to ground level? 4. A cylindrical gas tank is placed so that the axis of the cylinder is horizontal. If the tank is half full, find the force on a circular end of the tank, assuming that the diameter is 3 feet and gasoline has a density of 50 lb/ft 3 . 5 Find the centroid of the region bounded by the graphs of 2 4 ) ( x x f - = and 2 ) ( + = x x g . 6 Evaluate these integrals symbolically by hand! a) + dx x 9 2 4 b) + dx x x 9 2 4 c) + dx x x 9 2 2 4 d) + - dx x x 4 2 9 3 e) - - + dx x x x 6 2 7 f) + - - - dx x x x x x ) 4 2 )( 2 ( 8 4 3 2 g) xdx x 5 cos 2 sin h) - 2 9 2 x x dx i) xdx x ln 2 7. Evaluate the following improper integrals. State whether they converge or diverge. a) 1 2 1 dx x b) - 2 1 2 2 2 dx x x 8. Solve the following differential equation(s). a)

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Fin Ex REVIEW - Final Exam Review Math 272 Stewart 1 Find...

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