Worksheet on Improper Integrals PDF

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Shannon Patrick Sullivan...

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MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS

Improper Integrals

Math 1001 Worksheet

Winter 2017

For practise only. Not to be submitted. 1. Determine whether each of the following improper integrals converges or diverges, finding the value of those integrals that converge. Z ∞ 1 √ (a) dx 4x + 1 2 Z 4 1 √ (b) dx 4−x 0 Z 0 (c) e3x dx −∞ Z ∞ 1 (d) dx 3 1 (x + 3) 2 Z ∞ x dx (e) 4+1 x 0 Z 0 ex dx (f) x −∞ 1 + e Z 3 1 √ dx (g) 9 − x2 0 Z 3 x dx √ (h) 9 − x2 0 Z ∞ 1 (i) dx x ln2 (x) e Z 3 2 1 (j) dx 2+9 4x −∞ Z ∞ (k) xe−x dx 0 Z ∞ ln(x) √ dx (ℓ) x x 1...