Arrington1Math 0120Examination #3SampleName (Print) Student ID # .Signature ___________________________________________ Score .TA (Circle one)Instructions:1. Clearly print your name and sign your name in the space above.2. There are 8 problems, each worth the specified number of points, for a totalof 100 points. There are also two extra-credit problem worth 5 points and 10points.3. Please work each problem in the space provided. Extra space is availableon the back of each exam sheet. Clearly identify the problem for which thespace is required when using the backs of sheets.4. Show all calculations and display answers clearly. Unjustified answerswill receive no credit.5. Write neatly and legibly. Cross out any work that you do not wish tobe considered for grading.6. Calculators may not be used. All derivatives and integrals are to befound by learned methods of calculus.Arrington21. (12 pts.) Let f(x) =2x1.(a) Approximate the area under the curve y = f(x) from a = 1 to b = 7 using a Riemannsum with 2 left rectangles. (Write the sum; you need not evaluate it.)(b) Find the exact value of the area under the curve y = f(x) from a = 1 to b = 7 by evaluating anappropriate definite integral using the Fundamental Theorem of Integral Calculus2. (21 pts.) Find the following integrals:(a) dx)1ex(x235(b)2x1xdx(c)131)xe( dxArrington33. (16 pts.) Use substitution to find the following integrals:(a)xexdx(b)2183x2x3dx4. (6 pts.) Find the average value of f(x) =3xon [0,2].Arrington45. (8 pts.) The acceleration of a particle at time t seconds is given by a(t) = 2t + 4e-0.2tft./sec2. Findv(t), the velocity of the particle at time t, if its initial velocity (the velocity at time t=0) is 5 ft/sec.6. (14 pts.) Set up, but do not evaluate, integrals for the area(a) Between the curves y = x3and y = x2from x = -1 to x = 1.(b) Bounded by the curves y = x and y = 4x –x2.Arrington57. Given a demand function of d(x) = 300 –0.4x and a supply function of s(x) = 0.2x.(a) (3 pts.) Find the market demand (the positive value of x at which the demand function intersectsthe supply function).(b) (4 pts.) Set up, but do not evaluate a definite integral for the producers’ surplusat the marketdemand.8. (16 pts.) Use integration by parts to find:(a)xln dx(b)x3xe dxArrington6(5 pts) Extra-Credit : You may earn an extra 5 points by evaluating21dxxwithout using theFundamental Theorem of Calculus(10 pts) Extra-Credit : You may earn an extra 10 points by finding
View Full Document
Unlocking...