IntegralsByPartsRcg

# IntegralsByPartsRcg - 36.596510085667 6. (1 pt) Evaluate...

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Mike Truong WeBWorK @ Dept of Mathematics and Statistics @ SDSU WeBWorK problems. WeBWorK assignment 05IntegralsByPartsRcg due 02/12/2008 at 09:00am PST. 1. (1 pt) Use integration by parts to evaluate the integral. Z xe 2 x dx + C Correct Answers: 0.5 * (x * eˆ(2 * x) - 0.5 * eˆ(2 * x)) 2. (1 pt) Use integration by parts to evaluate the integral. Z 5 x cos ( 2 x ) dx + C Correct Answers: 5 * 0.5 * (x * sin(2 * x) + 0.5 * cos(2 * x)) 3. (1 pt) Use integration by parts to evaluate the integral. Z 5 x ln ( 5 x ) dx + C Solution: Let u = ln ( 5 x ) and dv = 5 xdx . Then du = 1 5 x · 5 dx = 1 x dx and v = 2 . 5 x 2 . Z 5 x ln ( 5 x ) dx = uv - Z v du = ln ( 5 x ) 2 . 5 x 2 - Z 2 . 5 x 2 1 x dx = 2 . 5 x 2 ln ( 5 x ) - Z 2 . 5 x dx = 2 . 5 x 2 ln ( 5 x ) - 1 . 25 x 2 + C . Correct Answers: 5 * 1/2 * (xˆ2 * ln(5 * x) - 1/2 * xˆ2) 4. (1 pt) Evaluate the indeﬁnite integral. Z e 7 x sin ( 3 x ) dx Correct Answers: -3/58 * (eˆ(7*x) * cos(3*x)) + 7/58 * (eˆ(7*x) * sin(3*x)) 5. (1 pt) Use integration by parts to evaluate the deﬁnite in- tegral. Z e 1 8 t 2 ln tdt Correct Answers:
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Unformatted text preview: 36.596510085667 6. (1 pt) Evaluate the denite integral. Z 4 te-t dt Correct Answers: 0.908421805556329 7. (1 pt) Use integration by parts to evaluate the integral. Z 8 1 t ln tdt Correct Answers: 21.7560752585626 8. (1 pt) Evaluate the indenite integral. Z x arctan ( 2 x ) dx Correct Answers: ((1 + 4*x2)/(2*4))*arctan(2*x) - x/(2*2) 9. (1 pt) Evaluate the indenite integral. Z x sin 2 ( 8 x ) dx Correct Answers: (8*x2 - x*sin(2*8*x) - cos(2*8*x)/(2*8))/(4*8) 10. (1 pt) Evaluate the indenite integral. Z ln ( x 2 + 10 x + 16 ) dx Correct Answers: (x + 2)*ln(x + 2) + (x + 8)*ln(x + 8) - 2*x Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 1...
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## This note was uploaded on 09/25/2010 for the course MATH 150 taught by Professor Shen during the Spring '08 term at San Diego State.

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