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ex5_6401

# ex5_6401 - (a R 2 π x 3 cos xdx(b R π e x cos(2 x dx(c R...

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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 π x 3 cos xdx ; (b) R π e x cos(2 x ) dx ; (c) R 2-3 | x | dx . 3. Find the following indeﬁnite 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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