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HW2Solutions - p 498#7 Since the function is odd all the an...

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p. 498, #7 Since the function is odd all the ' n a s are 0. Repeated integration by parts gives 3 3 2 2 3 4 cos 3 sin 6 cos 6sin sin n x nx n x nx nx nx nx x nx dx n so that 3 3 2 3 4 3 0 2 2 6 12 2 sin cos 1 n n n n b x nx dx n n n n 6 7 * 7 2 1 * * 2 2 * * 2 3 * * 2 4 * * 2 5 2 7 2 1 674.8 7 2 1 454.7 3 2 336.4 4 3 265.6 5 4 219.0 x dx E b E E b E E b E E b E E b
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p. 498, #8 (My solution) The function is even, hence all the ' n b s are 0. 0 0 0 0 1 0 1 2 3 4 5 * 2 1 2 sin 2 2 1 1 sin cos sin 1 sin 1 2 2 1 sin 2 0 cos 1 cos 1 1 1 1 1 1 1 1 1 , 2,3,4, 1 1 1 1 1 1 4 3 0 4 15 0 1 sin n n n n a x dx a x nx dx n x n x dx a x dx n n a n n n n n n n a a a a E x 2 0 * * 2 1 * * 2 2 * * 2 3 * * 2 4 8 2 0.595 2 1 0.595 3 2 0.0292 4 3 0.0292 5 4 0.00659 dx a E E a E E a E E a E E a
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Page 498, #8: (Solution Manual) Page 517, problem 5: 0 2 0 2 0 1 0 ) sin( ) cos( ) sin( ) sin( ) ( ) cos( ) sin( ) sin( 2 2 ) sin( ) ( 2 ) ( 1 0 1 4 / 1 0 2 / ) ( d x d x B x f dv v v dv v v f B x x x x x f Page 517, #8:
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