ex5_6401

ex5_6401 - (a) R 2 x 3 cos xdx ; (b) R e x cos(2 x ) dx ;...

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Problem Sheet 5 for 6401 Due Monday 24 Nov 2008, at the Problem Class. You should hand in solutions to all problems, but only some of them will be marked. 1. Prove the following identities for hyperbolic functions: (a) cosh(2 x ) = 2 cosh 2 x - 1; (b) sinh(2 x ) = 2 sinh x cosh x ; (c) (tanh x ) 0 = 1 cosh 2 x , where tanh x = sinh x cosh x . 2. Compute the following definite integrals:
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Unformatted text preview: (a) R 2 x 3 cos xdx ; (b) R e x cos(2 x ) dx ; (c) R 2-3 | x | dx . 3. Find the following indenite integrals: (a) R x-2 ( x 2-4 x +3) 3 dx ; (b) R 3 x 2 + x-5 x 2-4 x dx ; (c) R 4 x 2 +54 x +134 ( x-1)( x +3)( x +5) dx ; (d) R 1 1+ x 2 dx ; (e) R 1 x 2-3 dx ; (f) R x +1 1-x 2 dx . 1...
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This note was uploaded on 03/03/2010 for the course MATH 6401 taught by Professor Parnovski during the Fall '08 term at UCL.

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