# WA2 assignment sheet_MAT-232_nina.pdf - Name Nina Odunlami...

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Chapter 6 / Exercise 42
Essential Calculus: Early Transcendentals
Stewart
Expert Verified
WA 2, p. 1 Name: Nina Odunlami University ID: 0653999 Thomas Edison State University Calculus II (MAT-232) Section no.: 2018NOV MAT-232-OL011 2018NOV Calculus II (MAT-232-OL011) Semester and year: NOVEMBER 2018 Written Assignment 2 Answer all assigned exercises and show all work. Each exercise is worth 4 points. Section 6.2 4. Evaluate the integral. ln x xdx (use integration by parts) ln u x ; 1 du x , dv x , and 2 1 2 v x ln x xdx uv vdu 2 2 1 1 1 (ln )( ) ( )( ) 2 2 x x x dx x 2 2 1 1 1 ln ( )( ) 2 2 x x x x dx = 2 1 1 ln 2 2 x x xdx 2 2 1 1 ln 2 4 x x x C
##### We have textbook solutions for you!
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Chapter 6 / Exercise 42
Essential Calculus: Early Transcendentals
Stewart
Expert Verified
6. Evaluate the integral.
18. Evaluate the integral.
22. Evaluate the integral.
2 3 1 2 1 3 3 3 x u x e xe du 2 3 1 2 1 ( )( ) 3 3 3 3 x u u x e e du 2 3 1 2 ( ) 3 3 9 u x ue x e du 2 3 1 2 1 3 3 9 x u x e ue du (use integration by parts) 3 , 1, , u u u x du dv e v e 2 3 1 2 ( ) 3 27 x u u x e ue e 2 3 3 3 1 2 (3 ) 3 27 x x x x e xe e Solve for x 1 = 2 (3)(1) (3)(1) (3)(1) 1 2 (1) ((3(1) ) 3 27 e e e = 3 5 27 e x 0 = 2 (3)(0) (3)(0) (3)(0) 1 2 (0) ((3(0) ) 3 27 e e e = 2 27 3 5 27 e - 2 27 24. Evaluate the integral. x 4
WA 2, p. 3
WA 2, p. 4 46. Evaluate the integral using integration by parts and substitution. 2 ln(4 ) x x dx (use u-substitution) 2 4 , 2 u x du xdx …. 1 2 x du ln( ) x u dx 1 ln( ) 2 x u xdu ln( ) 2 x u du x ln( ) 2 u du 1 ln 2 udu (use integration by parts) 1 ln , , 1, u u du dv v u u 1 1 ln (ln )( ) ( )( ) 2 udu u u u u 1 ln 2 u u u u 1 ln 2 u u u 2 2 2 1 (4 )ln(4 ) (4 ) 2 x x x 2 2 2 2 1 (4ln(4 ) ln(4 ) 4 ) 2 x x x x C Section 6.3 8. Evaluate the integral. 4 sin ( 3) x dx (use u-substitution) 3, u x du dx 4 sin udu 2 2 (sin ) u du (use half-angle formula) 2 1 (1 cos2 ) 2 u du 2 1 (1 2cos2 cos 2 ) 2 u u du 2 1 (1 2cos2