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Unformatted text preview: (a) Z 2 dθ √ θ 3 + θ 2 (b) Z 4 4 + sin 4 x √ x dx (c) Z ∞ dy e 2 y + 5 y (d) Z 1 ex √ x dx 9 (8) Decide if the improper integral converges or diverges. (a) Z ∞ e dx √ x + 1 ln x (b) Z ∞ 1 ln x x 2 dx (c) Z ∞ 10 1 z 216 dz (d) Z ∞ 1 x √ 1 + x 5 dx 10 (9) Decide if the improper integral converges or diverges. (a) Z ∞∞ dx 4 x 2 + 4 x + 5 (b) Z ∞ 1 arctan x x 2 dx (c) Z ∞ 1 ( x + 2) 4 dx (d) Z 11 x + 1 3 √ x 4 dx 11 (10) The function f ( x ) = 1 √ 2 π Z x∞ et 2 / 2 dt is important in statistics. Show that the integral on the right converges for all real x ....
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 Spring '09
 HarvanshManocha
 Calculus, #, Logarithm, Riemann integral, Henstock–Kurzweil integral, Polytechnic Institute of NYU MA

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