Asg2_Sol - MATH 118 – Spring 2010 Assignment 2, Solutions...

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Unformatted text preview: MATH 118 – Spring 2010 Assignment 2, Solutions 1. Textbook, Page 506, Exercises 8.3, # 17, 25, 33. 33. 2. Textbook, Page 512, Exercises 8.4, # 7, 13, 33. 3. Textbook, Page 517, Exercises 8.5, # 1, 7. 4. Use the substitution x tan( / 2) to evaluate the following integral. 2 cos d 1 2dx 2dx x tan( ) dx ( ) sec 2 ( )d d 2 2 2 2 1 tan 2 ( ) 1 x 2 2dx d d dx x 2 1 x2 2 cos 2 cos 1 x 2 2 3 x 2 3 tan ( 3 ) C 1 2 1 x2 2 1 tan 1 ( tan( )) C 2 3 3 5. A charged rod of length L produces an electric field at point P(a, b) given by E ( P) La b 4 0 ( x 2 b 2 )3 / 2 a dx Here, is the charge density per unit length on the rod and 0 is the free space permittivity and b ≠ 0. Evaluate the integral to determine an expression for the electric field E(P). E ( P) La b 4 0 ( x 2 b 2 ) 2 a dx 3/ 2 dx b L a a ( x 2 b2 )3 / 2 4 0 Suppose I I dx . Using x b tan dx b sec2 d 2 3/ 2 (x b ) b sec2 d tan ( x / b) cosd sin C C C 3 3 b sec 1 tan 2 1 ( x / b) 2 b L a dx ( x / b) x La a ( x 2 b2 )3 / 2 4b 0 [ 1 ( x / b)2 ]x a 4 0 a ( L a) / b ( a ) / b ( L a) [ ] [ ] 4b 0 1 (( L a) / b) 2 4b 0 b 2 ( L a) 2 b2 a 2 1 (( a ) / b) 2 E ( p) ...
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Asg2_Sol - MATH 118 – Spring 2010 Assignment 2, Solutions...

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