Unformatted text preview: APPM 1360 Test 1 Spring 2008 INSTRUCTIONS: Books, notes, ﬂying monkeys and electronic devices are not
permitted. Write your (1) name, (2) instructor’s name, and (3) recitation section on the
front of your bluebook. Also make a scoring table, with places for 4 problems, plus a
total score. Work all 4 problems. Start each problem on a new page. Show your work. in your answers. A correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit. 1. (35 points)
a. Draw the region between the curve y = 4x+ x2 and the line y = —x and use that region to answer the following questions.
b. Write out the integral that would determine the area of the region between the two curves. Don’t carry out the integration.
c. Suppose you were to create squares above the region with the base of the squares
perpendicular to the X—axis. Write the integral that would determine the volume created by slicing. Don’t carry out the integration
d. Write the integral that would determine the volume created by rotating the region about the y-axis. Don’t carry out the integration
e. Write the integral that would determine the volume created by rotating the region about the line y = 5. Don’t carry out the integration 2. Integrate the following: (27 points) a) 2 2C—5 dx b) I(x2—3x)esxdx c) Iesmxcoshxdx
x +5x . . . 3. (18 points)
Consider the region between the two curves y = x2 — 4 and the x—axis. a) Draw the region
b) Find the center of mass of the region if the density is constant. 4. (20 points) a) Find the length of the curve y = cosh x on the interval [0,4] dy cos x b) Solve the differential equation: x—— = —2 , x>0
dx x y in egg. .. ...
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- Spring '06