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Unformatted text preview: Math 182 Chapter 6 Exam Retakes All work must be explained on the following exam. Unless otherwise noted, all answers must be exact. Calculators with graphing, symbolic or programmable features are not allowed. AREA CALCULATION Consider the region enclosed by y = ( x 3) 2 +3 , y = ( x 3) 2 3 , and y = 4 x 10 as shown below. Express the indicated region in terms of one or more definite integrals. Be certain to determine the correct values for the limits of your integral(s). DO NOT ATTEMPT TO EVALUATE YOUR INTEGRALS! We find the indicated x values as follows: (a) ( x 3) 2 + 3 = ( x 3) 2 3 ⇒ 6 = 2( x 3) 2 ⇒ ( x 3) 2 = 3 ⇒ x 3 = ± √ 3 ⇒ x = 3 ± √ 3 so a = 3 √ 3 (b) 4 x 10 = ( x 3) 2 3 ⇒ 4 x 10 = x 2 6 x + 9 3 ⇒ x 2 10 x + 16 = 0 ⇒ ( x 8)( x 2) = 0 ⇒ x = 8 or x = 2 so b = 2 (c) 4 x 10 = ( x 3) 2 + 3 ⇒ 4 x 10 = x 2 + 6 x 9 + 3 ⇒ x 2 2 x 4 = 0 ⇒ x = 1 ± √ 5 so c = 1 + √ 5 integraldisplay 2 3 √ 3 bracketleftBigparenleftBig ( x 3) 2 + 3 parenrightBig parenleftBig ( x 3) 2 3 parenrightBigbracketrightBig dx + integraldisplay 1+ √ 5 2 bracketleftBigparenleftBig ( x 3) 2 + 3 parenrightBig (4 x 10) bracketrightBig dx Math 182 Chapter 6 Exam Retakes All work must be explained on the following exam. Unless otherwise noted, all answers must be exact. Calculators with graphing, symbolic or programmable features are not allowed. VOLUMES Consider the region shown which is enclosed by y = ( x 2) 2 2 + 2 and y = x . Write down definite integrals but do not evaluate them! for the volume formed from this region in each of the following cases: The line crosses the parabola when x = ( x 2) 2 2 + 2 ⇒ 2 x = ( x 2) 2 + 4 ⇒ 2 x = x 2 4 x + 8 ⇒ x 2 6 x + 8 = 0 which implies that ( x 4)( x 2) = 0 so either x = 2 or x = 4....
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This test prep was uploaded on 04/08/2008 for the course MATH 182 taught by Professor Keppelmann during the Spring '08 term at Nevada.
 Spring '08
 Keppelmann
 Math

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