MAC 2312 Midterm: MAC2312 C96 Test 2
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June 19, 1996: for each of items 1, 2, 3, set up the integral (or integrals) whose value gives the indicated quantity; do not solve, (5 pts. ) Find the average value of f (x) : (10 pts. ) If x and y satisfy the parametric equations. Nd the arc length of the curve over the time interval [0, 2]. x = 4 3t + t2 y = 3 + 6t t2: (10 pts. ) A cylindrical tank is 18 m high, has cross sectional area a m2, and is 75% full of a liquid with density n/m3. Set up the integral giving the work done in pumping the liquid to the top of the tank. Leave your answer in terms of a and . e 2x dx = : (10 pts. ) = y3x; y(1) = 2: (15 pts. ) A cup of co ee is sitting on the desk. Solve the equation to nd the temperature function.
