1 Cabin. Professor: What is. Student: ln Cabin oh Log Cabin! Professor: No. Log Cabin + C = A Houseboat!

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1 MATH 4 Sprig 0 Exam # Tuesday March st Sectios: Sectios ; 6.8; Name: Score: = 00 Istructios:. You will have a total of hour ad 50 miutes to complete this exam.. A No-Graphig Calculator may be used o the exam. 3. Show ALL of your work. I give out partial credit. 4. Cheatig of ay kid o the exam will ot be tolerated ad will result i a grade of 0%. 5. If you have a questio, please come up ad ask it is much better to ask right away tha to stay stuck for a log period of time. 6. Take a deep breath, relax, ad good luck!! Professor: What is Cabi dcabi Studet: l Cabi oh Log Cabi! Professor: No. Log Cabi + C = A Houseboat! Morale of the story Do t forget your + C s!!!!!!!!!!

2 Short Aswer Sectio The followig problems will be graded as right or wrog. No eed to show work. ( poits each) a) Give the velocity fuctio for a object is v ( t) = o [ 0,8] ad s ( 0) = t + 4. Determie the positio fuctio s (t) for the object. s(t) = b) If you have a itegral that ivolves the term 36 x you cosider that may simplify it?, what substitutio would x = c) Give the appropriate form of the partial fractio decompositio for the followig ratioal fuctio (No eed to solve for ay ukows A, B, C, etc.; just set it up properly). 4 3 x + x = d) True or False: = x l x + + c x + e) Fid the mass of the thi bar with the desity fuctio ρ ( x ) = + si( x) for 0 x π. m =

3 Show Your Work Questios The followig questios should be aswered to the best of your ability. Show work where you ca as partial credit will be awarded i some cases.. For the followig, assume t is time measured i secods ad that the velocity has uits of m / s. Give the velocity fuctio v( t) = 0si( t) ad 0 t π fid: (5 poits each). a) The displacemet over the iterval. b) The distace traveled over the iterval.

4 . Fid the area betwee the below curves o the iterval [0, ]. Give a rough sketch of the regio (you may chage the scale o the coordiate grids if eeded). (5 poits each). a. y = x +, y = 3x b. x = y, x =

5 3. Set up the itegral eeded to fid the volume of the solid formed by revolvig the regio about the give lie. You should also draw a rough sketch of the resultig figure (you may chage the scale o the coordiate grid if eeded). You DO NOT eed to evaluate the itegral (just set it up). (6 poits each) Regio bouded by a. About the x-axis y x =, y =, ad x = 0 b. About the lie x =

6 5. Set up ad simplify the itegral that you would use for fidig the arc legth of the graph of = x poits). y from x = 3 to x = 4. Do ot evaluate the itegral. (5 6. The homicide rate decreases at a rate of 3% per year i a city that had 800 homicides per year i 00. At this rate, whe will the homicide rate reach 600 homicides per year? (6 poits).

7 9. Evaluate the followig itegrals usig ay techique you have available (6 poits each). a) x si(x) b) e x si x

8 c) si (x) 0. Evaluate the followig itegrals usig ay method you kow (6 poits each). a. π ta ( x)sec ( x)

9 3 5 b) si ( x )cos ( x) c) 0 x + 6

10 . Trasform the followig itegral ito a itegral ivolvig trigoometric fuctios (No eed to evaluate the itegral, just set it up properly ad reduce ito a form which is easy to itegrate). (5 poits). x 6 x. Evaluate the followig itegral by the method of partial fractios. (6 poits). x x 6

11 My Gift To You Importat Itegrals. ta( x ) = l cos( x) + C. sec( x ) = l sec( x) + ta( x) + C 3. cot( x ) = l si( x) + C 4. csc( x ) = l csc( x) + cot( x) + C Reductio Formulas si ( x)cos( x) = si ( x). si ( x) + cos ( x)si( x) = cos ( x). cos ( x) + ta ( x) = ta ( x) 3. ta ( x) sec ( x) ta( x) = sec ( x) 4. sec ( x) +

MATH 2411 Spring 2011 Practice Exam #1 Tuesday, March 1 st Sections: Sections ; 6.8; Instructions:

MATH 2411 Spring 2011 Practice Exam #1 Tuesday, March 1 st Sections: Sections ; 6.8; Instructions: MATH 411 Sprig 011 Practice Exam #1 Tuesday, March 1 st Sectios: Sectios 6.1-6.6; 6.8; 7.1-7.4 Name: Score: = 100 Istructios: 1. You will have a total of 1 hour ad 50 miutes to complete this exam.. A No-Graphig