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138assgn3

# 138assgn3 - MATH 138 Assignment 3 More denite integrals...

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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) 1 0 arctan x 1+ x 2 dx . (b) 4 1 dt (2 t +1) 3 . (c) ( * ) 1 0 e 3 x dx . (d) sin(In t ) t dt . (e) ( * ) π 2 0 sin 3 θ cos 2 θ dθ . (f) ( * ) x sec x tan x dx . 2. The functions f ( x ) = e x 2 and g ( x ) = x 2 e x 2 don’t 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 (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) ( * ) 1 0 dx 1 - x 2 . (b) ( * ) 0 dz z 2 +3 z +2 . (c) ( * ) -∞ (2 - v 4 ) dv . (d) 5 e - y 2 dy (e) ( * ) 1 0 e 1 x x 3 dx . (f) -∞ x 3 e - x 4 dx . (g) 0 -∞ 1 2 x - 5 dx . (h) ( * ) 1 - 1 dx x 2 - 2 x . (i) 1 0 1 4 y - 1 dy . (j) ( * ) 2 e - x x dx .

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138assgn3 - MATH 138 Assignment 3 More denite integrals...

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