Ch. 6 Test

# Ch. 6 Test - Math 182 Chapter 6 Exam All work must be...

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Unformatted text preview: Math 182 Chapter 6 Exam 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. Be certain to do all trigonometric calculations in Radians. PROBLEM POSSIBLE EARNED AREA CALCULATION 20 VOLUMES 20 ARC LENGTH 20 ROPE WORK 15 HYDROSTATIC FORCE 15 PROBABILITY 10 TOTAL 100 EXTRA CREDIT 5 AREA CALCULATION Consider the region enclosed by y = 0 , y = ( x- 2) 2- 2 and y = 2 x- 3 . DO NOT CONFUSE THIS WITH THE REGION ENCLOSED BY JUST y = 2 x- 3 AND y = ( x- 2) 2- 2 . Sketch this region and find one or more integrals for its area. DO NOT EVALUATE YOUR INTEGRALS. We must first see where these two curves intersect: 2 x- 3 = ( x- 2) 2- 2 ⇒ 2 x- 3 = x 2- 4 x + 2 ⇒ x 2- 6 x + 5 = ( x- 1)( x- 5) = 0 So either x = 1 or x = 5. When x = 1 we have that y = 2 · 1- 3 =- 1 and when x = 5 we have that y = 2 · 5- 3 = 7. We must further examine where the parabola and line cross the x-axis. Now 2 x- 3 = 0 ⇒ x = 3 2 and ( x- 2) 2- 2 = 0 ⇒ x 2- 4 x + 2 = 0 ⇒ x = 4 ± √ 16- 8 2 = 2 ± √ 2 If we integrate with respect to x then we must split the region into two calculations as follows: integraldisplay 1 2- √ 2 bracketleftBig- parenleftBig ( x- 2) 2- 2 parenrightBigbracketrightBig dx + integraldisplay 3 2 1 [0- (2 x- 3)] dx VOLUMES Consider the region enclosed by y = sin x, y = cos x...
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Ch. 6 Test - Math 182 Chapter 6 Exam All work must be...

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