Select the correct answer. Which is the correct solution for the integral |2 asinade? O A. -1 OB. 2 OC. 0 OD. 12 Select the correct answer. Which integral will require Integration by Parts only once? O A . [(1-x2je2xox O B. [x282Xox O C. [(-x je 2 x x OD. [- x2e2xox3 Select the correct answer. Which is the correct choice for dv if you evaluate | x cosx dx using Integration by Parts? OA. COSX O B. - OC. x'dx OD. -1Select the correct answer. 2 Which is the correct solution for the integral 12: dz ? 9 A. e"(-2+2z-z')+C B. e"(-2+2z+z')+C c. e"(-2- 22-23 )+C D. e\"(-2-22+z')+C 5 Select the correct answer. Which should you substitute as u when evaluating | tan* xsec x dx ? OA. sec xtan x O B. sec x O C. sec2x O D. tan X6 Select the correct answer. [ sec " xtan" xox if the power of tan x is odd, what should you substitute for u? When evaluating secm xtan xox O A. cot x OB. sec x O C. tan x OD. COS X7 Select the correct answer. rating [sec' xtan" xdx if the power of sec xis even, what should you substitute for u? OA. cot x OB. sec x OC. tan x OD. cos X8 Select the correct answer. Evaluate: ((1-cos2 x ) 4 dx sin* x O A. X - sin 2x + - sin 4x 001 +0 4 OB. N/ W X + sin 2x - NI - sin 2x +C 4 O C. X - Sin 4X + - sin 2x +C 4 OD. X - Sin4X + - Sin4x NI - +C 4Select the correct answer. Which is the correct trigonometric substitution for evaluating I\" x2 + 64 dx ? A. x = 8sec 9 B. x = 8tan 9 C. x = 8sin9 D. X = 8 tan 9 10 Select the correct answer. Which of the following integrals require you to substitute x = 6tan@ to easily integrate? O A. - dix 136+ x2 OB. dx 136 - X2 OC. 1 dx 16-x2 OD. 1 ax 16+ x211 Select the correct answer. Which is the correct trigonometric substitution for evaluating dx ? VX + 6x + 25 O A. X = 1/25 tane OB. x = 25tane OC. x= 4tan0-3 OD. X = 16tane12 Select the correct answer. Which is the correct trigonometric substitution for evaluating I416 x2dx? A. x = 4 sec 9 B. x = tan 9 C. x = 4 sine 4 D. X = W 13 Select the correct answer. 3 Which correctly shows the rational expression 2X +1 after applying the long division method? x+2 O A, -4x+1 2x+, x +2 14 Select the correct answer. Evaluate the integral ax . X +2 OA. 8In | x +21-x3+3x2 -12x +C 3 OB. 8In | x+ 21-x3+3x2 - 4x +C 3 O C. 24In | x + 21-x3 +3x2-12x +C 3 OD. 24In | x + 21-x3 +3x2 -4x +C 315 Select the correct answer. Evaluate the integral | 2x + 1 dx . (x - 1) (x2 + 1) O A. NIW In | x +11 - - In1 x2 +1/ +sec- (x2 +1)|+c OB. N/W In | x + 1| - -In | x2 +1/ + sec-1(x )|+C N O C. N/ W In | x - 11 - - In| x2 + 11 + tan -1(x2 + 1))+c OD. N/ W In | x - 11 - - In| x2 +1|+tan- (x)+C N16 Select the correct answer. X Evaluate the integral dx . x 2 - 6x +8 O A. In| x - 4| - In| x - 2| + C B. 2In | x - 4| - In| x - 2| + C O C. 2In | x - 4| - 2In | x - 2| + C O D. 2In| x - 2| - In | x - 4| + C17 Select the correct answer. Which integral resembles [ x2 x2 - 90x? O A . 42 Jaz +urdu = " (a2 + 202 Waz + uz - a In(u + vaz + u= ] + 0 OB. Ja2 + u2 du = a2 NIS + 2 In( u + Vaz + u2 ) + 0 O C. Vu2 - a2 du = a2 NIS VU2 - 22 2 In ju + Vuz - a2 + 0 OD. 42 Juz - a2 du =4(242 -a2Wuz - a2 - a_Inju+ vuz - a2 + C18 Select the correct answer. Using the table of integrals, solve dx . cos(x + 7) O A. In|sec(x + 7) + tan(x + 7) | + C O B. In| sec(x + 7) - tan(x + 7) | + C O C. 7In | sec(x + 7) + tan(x + 7) | + C O D. In|sec7x + tan7x| + C19 Select the correct answer. Which integral resembles 5(20594152 sin 5x O A. [cot udu = - 1 cot"- u - Scot - 2 udu n- 1 OB. [sin udu = - - sinucosu + n-1 [sinn -2 you n n OC. [cosh udu = - cos"- usinut n -1 Icon - 2 udu n n OD. Stan 2 udu = tan u - U + C20 Select the correct answer. Using the table of integrals, solve 1 13 dx . sin x O A. | - csc x cotx - -Incsc x - cotx| + C 2 N OB. | - -CSC X cotx + -Incsc x - cot x + C 2 2 O C. sin x cot x + -In sin x - cotx/+ C NI - 2 OD. w / - csc x cotx + -Incsc x - cotx|+ C 321 Select the correct answer. Which is the most appropriate integration method for solving | cost x sin$ x ox ? O A. Integration by Parts O B. Integrating expressions with powers of sine/cosine O C. Basic Substitution O D. Trigonometric Substitution22 Select the correct answer. Which is the most appropriate integration method for solving 16- x2 ox ? x 2 O A. Integration by parts O B. Integrating expressions with powers of tangent/secant O C. Long Division and Partial Fractions O D. Trigonometric Substitution23 Select the correct answer. Using the strategy to select the best integration techniques, evaluate the integral | cos* xtan x dx. O A. sin* x +C 4 OB. sin* x +C 4 OC. sin* x 4 OD. sin x +C 424 Select the correct answer. Using the strategy to select the best integration techniques, evaluate the integral |2sin(2x + 3 )dx . O A. - cos(2x + 3) + C O B. 2 cos(2x+ 3) + C O C. sin(2x+ 3) + C O D. 2 sin(2x) + C25 Select the correct answer. Approximate the integral | ecosox using midpoint rule, where n = 4. O OA. 2.381 OB. 2.345 O C. 2.336 O D. 2.43626 Select the correct answer. Approximate the integral | In( (x +3) )dx using trapezoidal rule, where n = 5. O O A. 0.655 O B. 0.624 O C. 0.638 OD. 0.64527 Select the correct answer. An architect is trying to nd the area of a swimming pool. For that he realized he needs to nd the area under the curve from 0 to 2 of sin(x2) + 1. Estimate the area using midpoint rule, where n = 4. A 2.837 B 2.744 " C. 2.556 D 2.806 28 Select the correct answer. Approximate the integral | cos(x )dx using Simpson rule, where n = 4. O A. 0.905 O B. 0.908 O C. 0.895 OD. 0.83829 Select the correct answer. G) 1 Determine whether the p integral 110} is convergent or divergent. 0X2 A. It will diverge because of the Limits. B. It will converge because P > 1- C. It will converge because p D. It will diverge because p = 4. 30 Select the correct answer. 0 Which statement best describes why [#43: will converge or diverge? 3x-6 A. It will converge, because the corresponding limit exists. B. It will diverge, because the corresponding limit does not EXiSt. C. It will converge because the corresponding limit does not EXiSt- D. It will diverge because the corresponding limit exists. 31 Select the correct answer. 2 x-3 3 Evaluate the Integral I d): and then state whether it converges or diverges. 3 A. 24% ,It will converge. B. 4J5 , It will diverge. C. 00 ,It will diverge. D. 45 , It will converge. 32 Select the correct answer. 7 Evaluate the Integral ox and state whether it will converge or diverge. VX - 4 O A. 2, It converges. O B. 14, It diverges. O C. co , It diverges. O D. 14, It converges