# Sketch give a geometric interpretation for 2 z 1 x 1

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Chapter 1 / Exercise 67
Precalculus: A Concise Course
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7. Sketch, give a geometric interpretation for2Z|x-1|dxand evaluatethis definite integral.
11. Give a geometric interpretation for3Z9-x2dxand evaluate thisdefinite integral.
13. FindddxxZ11 +t3dt1
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Chapter 1 / Exercise 67
Precalculus: A Concise Course
Larson Expert Verified
14.Zdx(arctanx)(1 +x2)15.Z11-x2dx16.Zx1-x2dx17.Z11 +x2dx18.Zx1 +x2dx19.Z1x2+ 9dxVI.Applications of Integration1. Find the volume of the solid that results when the area of the regionenclosed byy= 2x,x= 0, andy= 2 is revolved aboutx= 1.2. Find the volume of the solid that results when the region enclosed byy=x3andx=y3is revolved about thex-axis.3. A cylindrical tank 8 feet in diameter and 10 feet high is filled withwater weighing 62.4 lbs/ft3. How much work is required to pump thewater over the top of the tank?4. A spring whose natural length is 2.5 m exerts a force of 100 N whenstretched 40 cm. How much work, in joules, is required to stretch thespring from its natural length to 4 m?5. A 50 foot chain weighing 10 pounds per foot supports a beam weighing1000 pounds. How much work is done in winding 40 feet of the chainonto a drum?6. Water is being drawn from a well 100 ft deep, using a bucket thatscoops up 100 lb of water. The bucket is being pulled up at a rate of2 ft/s, but it has a hole in it bottom through which water leaks out athe rate of .5 lb/s. How much work is done in pulling the bucket to thetop?7. Find the length of the curvef(x) =x3/2+ 2 for 0x4/3.8. Find the centroid of the plane region bounded by the curvesy= 2x4andy=x2+ 1
VII.Hyperbolic Functions1. Findy0fory=x2+ 4coshx2.Zexsinh(ex)dx
Math 121Outline AnswersI.Pre-Calculus1.(a)f(3) = 0(b)g(-2) = 2(c)fg(-2) = 0(d)gf(3) = 02.(a) Both have slope of 9/4.(b) One has slope of 9/4 the other has slope of -4/9.3. Some very pretty pictures.4.x= 6, y= 35.k= 296.x6=-1II.Limits and Continuity1. 122. 1/33. 104. 1/45. 06. 17. 1/128. 09.x=-2,110.k= 1/211.k= 5III.Differentiation1.f0(x) =-20x2.f0(x) =(x2+x-2)(2x)-(x2-1)(2x+ 1)(x2+x-2)2
23.f0(x) = 4x324. 4.925.dydx=3x2-6y6x+ 3y2IV.Applications of Differentiation1.(a) 3.49 MPH(b) receding at 7.58 MPH2.(a) Increasing: (3,) and decreasing: (-∞,0)(0,3)(b) Concave up: (-∞,0)(2,) and concave down: (0,2)(c)x= 0,23. (a) -4 ft/sec (b) 2 ft/sec4.r=3q30π, h=1003900π5. 22×26.r= 2, h= 5/37. 24 feet/sec8.9.5310. 311.2312. 113.1214. 0V.Integration
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