ex4_6401

ex4_6401 - (a) R x 2 sin(2 x ) dx ; (b) R 1 x 2 1+ x 2 dx ;...

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Problem Sheet 4 for 6401 Due Monday 17 Nov 2008, at the Problem Class. You should hand in solutions to all problems, but only some of them will be marked. 1. We define Z 1 x - a dx = lim N →∞ Z N 1 x - a dx, if the limit in the right-hand side exists (and is finite). Find for which a this integral exists and compute it. 2. Compute the following definite integrals:
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Unformatted text preview: (a) R x 2 sin(2 x ) dx ; (b) R 1 x 2 1+ x 2 dx ; (c) R 2 1 ( 2 x 2 / 3-3 x 3 / 2 ) dx . 3. Find the following indenite integrals: (a) R x 17 ln xdx ; (b) R arctan xdx ; (c) R sin 5 xdx ; (d) R cos 2 xdx ; (e) R cos 4 xdx ; (f) R e 2 x arcsin( e x ) dx . 1...
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