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# Math141 Exam 1 Study Guide MATH141

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This 3 page Study Guide was uploaded by Benjamin Mao on Monday February 8, 2016. The Study Guide belongs to MATH141 at University of Maryland taught by Dr. Gulick in Spring 2016. Since its upload, it has received 156 views. For similar materials see MATH141 in Math at University of Maryland.

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Date Created: 02/08/16

Math141 Exam 1 Study Guide b b Volume Formulas: a A(x)dx , a A(y)dy b Work Formula: ∫ F(x)dx a b ∫ f x)−g x)dx Area for moments: a b M 1 2 2 x : ρ∫a2 [f (x] [ g(x])dx b My:∫ x[f(x−g(x) ]x a M M ´ ´ ¿ y, x ( : (A A ) b ' 2 Arc Length: ∫a√1+ [f (x]dx b dx 2 dy2 Arc Length (Parametric): ∫ ( )( ) dt a √ dt dt Problems: 1) Determine the volume of the solid obtained by rotating the region bounded by y=2 √−2 and y=x−2 x=−2 about the line . 1kg/m 2) A cable that weighs 2 is lifting a load of 180kg up a shat that is 40m deep. How much work is required to lift the load all the way up the shaft? 3) A tank of water is 20 feet long and has a cross section in the shape of an equilateral triangle with sides 4 feet long (point of the triangle points directly down). The tank is filled with water to a depth of 10 inches. Determine the amount of work needed to pump all of the water to the top of the tank. Assume that the density of water is 62.5 lb/ft . 3 4) Find the center of mass for the triangle with vertices (0, 0), (-4, 2) and (0,6). x=4si( ) ,y=1−2co( ) −52π≤t≤34π 5) 4 4 Provide the following information… (i) A sketch of the parametric curve (including direction of motion) based on the equation you get by eliminating the parameter. (ii) Limits on x and y. (iii) A range of t’s for a single trace of the parametric curve. (iv) The number of traces of the curve the particle makes if an overall range of t’s is provided in the problem. 6) Set up, but do not evaluate, an integral that gives the length of the parametric curve given by the set of parametric equations. You may assume the curve traces out exactly once for the given range of t’s. x=cos ( ), y=si1−t2)− ≤t≤0 2 5/3 7) Determine the length of y=10 8+x ) 167≤ x≤953 Note: Some problems taken from Paul’s Online Notes

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