MDN: MAC2233, Practice Test 4 Name:______________________________MDN: MAC2233, Practice Test 4 Name:______________________________Chapters 5.1 – 5.5 Date: Show all possible work on this test paper.1. Evaluate ( )x x dx- +�58 4 7.2. Find the function whose tangent line has the slope -39 4x for each value of x, and whose graph passes through (3, -2).3. Evaluate xe dxx-� �-� �� ��854. Evaluatex dxx x� �- +� �� ��3535 5775. Evaluate xdxx -�56346. Evaluate ( )xx e dx�98Page 1 of 87. Evaluate the indicated integral:x xdxx x x+ ++ + +�4 35 43 12 65 10 128. Evaluate xdx� �+� �� ��3738Page 2 of 89. Evaluate ( )x-+�5627 3 . Express your answer as a decimal. Approximate to one decimal. 10. Evaluate dxx x� �+ -� �� ��5528 95.11. Evaluate x dxx� �+� �+� ��73411512. Evaluate dxx+�34135 2 Approximate your answer to two decimal places.13. Determine the area of the region bounded by the curves y = 2 + 5x – 2/3x2 and y = x2 + 2. (Hint: Sketch the graph or solve the two equations simultaneously.)Page 3 of 814. Sketch the region R and then use calculus to find the area of R. R is the region between the curve y = x4 and the line y = 15x - 14 for x  0 .15. Find the Gini index for the given Lorentz curve: L(x) = 0.2x2 + .25x.16. Find the average value of xx-35 over the interval 1 ≤ x ≤ e3 17. At a factory a machine that is t years old is generating revenue at a rate ofR’(t) = 20,000 – 50t2 dollars a year and is generating costs at a rate of C’(t) = 5,000 + 10t2 dollars a year. [a] What is the useful life of the machine(round to nearest year), and [b] compute the net profit generated by themachine over its useful life.18. Money is transferred continuously into an account at a constant rate of $4,500 a year. The Account earns interest at the annual rate of 5.5% compounded continuously. How much Will be in the account at the end of 35 years?Page 4 of 8KEYShow all possible work on this test paper.1. Evaluate ( )x x dx- +�58 4 7.( )xx xx x x C= - + = - + +62 6284 47 2 76 2 32. Find the function whose tangent line has the slope -39 4x for each value of x, and whose graph passes through (3, -2).( )( )- + - = - + =-449 394 (3, 2) 4 3 24 4xx C F CC = -172.25- -494 172.254xx3. Evaluate xe dxx-� �-� �� ��85lnxe x C-=- - +81584. Evaluatex dxx x� �- +� �� ��3535 577--� �� �� �� �- + = - +� �� �� �-� �� �� �= + + +� � �8253358525 1 57 5 7 5 ln37 2 755ln35 53 2 7x xx x dx xxxxCx5. Evaluate xdxx -�5634u = x6 – 4 du = 6x5dx dx = (6x5)-1 du= = = - +� �5653 1 1 1 1 1ln ln 46 2 2 2xdu u x Cu x uPage 5 of 86. Evaluate ( )xx e dx�98u = x9du = 9x8 dx dx = (9x8)-1� �= = = +� �� �� �9881 1 1 19 9 99u u u xx e du e e e Cx7. Evaluate the indicated integral:x xdxx x x+ ++ + +�4 35 43 12 65 10 12u = x5 + 5x4 + 10x + 12 du = 5x4 + 20x3 + 10 = 5(x4 + 4x3 + 2) dx( )( )� �+ +� �� =� �+ +� �+� �4 34 33 4 21 3 155 4 25 4x xdu duu ux x3 3= ln u = ln x + 5x + 10x + 12 C5 58. Evaluate xdx� �+� �� ��3738u = � �+� �� �38xdu = 1/8 dx dx = 8 du( ) ( ) ( )� �= = = = +� �� �� �10 10107 773 37 71078 56 288 8 310 5 8u u xu du u9. Evaluate ( )x-+�5627 3 . Express your answer as a decimal. Approximate to one decimal.u = 7x + 3 du = 7 dx dx = 1/7du( )( )( )- --+� �= = =� �� �- -= =� �5775 36 62 12777 31 17 7 7 7 4938 112, 335, 409, 58749xuu du u du Page 6 of 810. Evaluate dxx x� �+ -� �� ��5528 95.( ) ( )( )--� �+ - = + - = + +� �-� �� � � �� � � �� � � �= + + - + + = - - -� � � �� � � �� � � �� � � �= - - = -� � �445418 84 481 95 8 9 5 8 ln 9 5 8ln449 9 20, 489 2920 ln 4 5 8ln1 ln 4 01024 44 4 4 120,489 29 13,065ln 4 ln 65,5361024 4 1024xx x x x xxx11. Evaluate x dxx� �+� �+� ��734115u = x + 5 du du = 1 dx du = dx( )( )( )( )( ) ( )-++ + = + = + +� � � �� � � �= + + - + + �� � � �� � � �� �717 724 43 1 17 72 241 117 74 4545 2 57 174 24 7 4 12 7 5 2 1 5 18.677 7xt xx x x12. Evaluate dxx+�34135 2 Approximate your answer to two decimal places.u = 5x+2 du = 5 dx dx = 1/5 ( ) ( ) ( )( )( )( )( )( ) ( )- --� �= = = +� �� �� � � �� � � �+ - + = -� � � �� � � �� � � �� � � �= - =� �343 33 34 44 43341 13 14 431 1411 3 3 43 5 25 5 5 54 4 4 45 3 2 5 1 2 17 75 5 5 56.6977 3.4428 3.2549uu du u x13. Determine the area of the region bounded by the curves y = 2 + 5x – 2/3x2 and y = x2 + 2. (Hint: Sketch the graph or solve the two equations simultaneously.)( )( )� � � �� � � �+ - - + = - = -� � � �� � � �� � � �� � � �� �= - = - - =� �� �� �2 33 32 2 20 032 302 5 5 52 5 2 53 3 2 3 35 5 45 1515 02 9 2 2x xx x x dx x x dxx xPage 7 of 814. Sketch the region R and then use calculus to find the area of R. R is the region between the curve y = x4 and the line y = 15x - 14 for x  0 .( )( )� � � �- - = - - = - - - - - =- - - =� � � �� � � ��22 5241115 32 15 115 14 14 30 28 14 4.4 6.7 2.32 5 5 2 5x xx x dx x 15. Find the Gini index for the given Lorentz curve: L(x) = 0.2x2 + .25x.GI = …