Practice Gateway 5

Adam Miller 107-Fall-2021 Assignment 107 Practice Gateway due 09/23/2021 at 11:07am CDT Problem 1. 2. (1 point) Find Z 3 2 8 t 3 + 2 t dt Answer: help entering equations Solution: 2 . 66667 t 3 + 2ln ( t ) 3 2 = 51 . 4776 Answer(s) submitted: • (72+2ln(abs(3)))-(64/3+2ln(abs(2))) (correct) Correct Answers: • 51.4776 Problem 2. 4. (1 point) Find Z 1 0 2 + 2 xdx Answer: help entering answers Solution: ( 2 + 2 x ) 2 4 1 0 = 3 Answer(s) submitted: • 3 (correct) Correct Answers: • 3 Problem 3. 5. (1 point) Find Z ( z - 2 ) sin ( 2 z + 9 ) dz Answer: help entering equations Do not include a constant of integration in your answer. Solution: 1 4 sin ( 2 z + 9 ) - ( z - 2 ) cos ( 2 z + 9 ) 2 Answer(s) submitted: • (z-2)(1/2cos(2z+9))+(1/4sin(2z+9)) (incorrect) Correct Answers: • 1/4*sin(2*z+9)-(z-2)*cos(2*z+9)/2 Problem 4. 6. (1 point) Find Z 2 u + 6 u 2 - 2 u du Answer: help entering equations Do not include a constant of integration in your answer. Solution: 5ln ( | u - 2 | ) - 3ln ( | u | ) Answer(s) submitted: • -3ln(abs(u))+5ln(abs(u-2)) (correct) Correct Answers: • 5*ln(|u-2|)-3*ln(|u|) Problem 5. 3. (1 point) Find Z e - v ( 2 - 2 e - v ) 4 dv Answer: help entering equations Do not include a constant of integration in your answer. Solution: ( 2 - 2 e - v ) 5 10 Answer(s) submitted: • (2-2eˆ-v)ˆ5/10 (correct) Correct Answers: • [2-2*eˆ(-v)]ˆ5/10 Problem 6. 7. (1 point) Find Z 12 v v 2 + 8 v + 20 dv Answer: help entering equations Do not include a constant of integration in your answer. Solution: 6ln ( v + 4 ) 2 + 4 - 24tan - 1 ( v + 4 2 ) Answer(s) submitted: • -12ln(abs(2/sqrt((v+4)ˆ2+4)))-24arctan((v+4)/2) (correct) Correct Answers: • 6*ln((v+4)ˆ2+4)-24*atan((v+4)/2) Problem 7. 1. (1 point) Find Z 7 u 4 + 3 1 + u 2 + e 4 u du Answer: help entering equations Do not include a constant of integration in your answer. Solution: - 7 3 u - 3 + 3tan - 1 ( u )+ 1 4 e 4 u Answer(s) submitted: • -7/3uˆ-3+3arctan(u)+1/4eˆ(4u) (correct) Correct Answers: • -7/3*uˆ(-3)+3*atan(u)+1/4*eˆ(4*u) 1