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Unformatted text preview: MATH 138 Assignment 3 Spring 2009 More definite integrals. Improper integrals. Submit all problems marked (*) by 12:30 p.m. on Friday, May 29. 1. Evaluate the following definite integrals. You may find useful to read Section 7.5 from the book, Strategy of integration. (a) R 1 arctan x 1+ x 2 dx . (b) R 4 1 dt (2 t +1) 3 . (c) ( * ) R 1 e 3 x dx . (d) R sin(In t ) t dt . (e) ( * ) R 2 sin 3 cos 2 d . (f) ( * ) R x sec x tan x dx . 2. The functions f ( x ) = e x 2 and g ( x ) = x 2 e x 2 dont have elementary antiderivatives (read Can we integrate all continuous functions?, on page 487 of the book!), however, h ( x ) = (2 x 2 +1) e x 2 does have. Evaluate R (2 x 2 + 1) e x 2 dx . 3. Explain why each integral is improper. Determine whether they are convergent or divergent and evaluate the convergent ones. (a) ( * ) R 1 dx 1- x 2 . (b) ( * ) R dz z 2 +3 z +2 ....
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