Unformatted text preview: improper integral converges or diverges . If it converges, specify its value. Z t 1 ln x x 2 dx = ( using “parts” ) =ln t t1 t + 1. Therefore, Z ∞ 1 ln x x 2 dx = 5. (10) Show all your work in determining the value (if it exists) of the following improper integral. If it diverges show your work in determining this. Z 3 2 3 √ x2 dx 6. (8) Use the comparison thoerem, explaining how it applies, to determine whether the integral is convergent or divergent . You DO NOT need to evaluate the integral. (You may use, without proof, any knowledge about convergence or divergence of the improper integrals involving 1 /x , 1 /x 2 , ex , etc., but be speciﬁc.) Z ∞ 1 sin 2 x x 2 dx...
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 Winter '98
 MathDep
 Integrals, Tn, 6 pts, 4 pts, dx, Riemann integral, Henstock–Kurzweil integral

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