1124worksheet7

# 1124worksheet7 - (a Z 2 dθ √ θ 3 θ 2(b Z 4 4 sin 4 x...

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Polytechnic Institute of NYU MA 1124/1424 Worksheet 7 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 1

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2 (1) Calculate the integrals, if they converge. (a) Z 1 2 7 x + 4 dx (b) Z 0 1 ( x + 2)( x + 3)
3 (2) Calculate the integrals, if they converge. (a) Z e 1 x (ln x ) 2 dx (b) Z π/ 4 0 cos x sin x dx

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4 (3) Calculate the integrals, if they converge. (a) Z 2 - 2 1 x 2 - 1 dx (b) Z 5 4 1 (5 - x ) 2 / 5 dx
5 (4) Calculate the integrals, if they converge. (a) Z 9 1 1 3 x - 9 dx (b) Z 3 -∞ 1 x 2 + 9 dx

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6 (5) Find the values of p for which the integral converges and evaluate the integral for those values of p . Z e 1 x (ln x ) p dx
7 (6) Decide if the improper integral converges or diverges. (a) Z 1 cos 2 x x 2 dx (b) Z 1 1 x 3 + 5 dx (c) Z π/ 2 0 dx x sin x (d) Z 1 2 - x 2 dx

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8 (7) Decide if the improper integral converges or diverges.

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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 e-x √ 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 2-16 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 1-1 x + 1 3 √ x 4 dx 11 (10) The function f ( x ) = 1 √ 2 π Z x-∞ e-t 2 / 2 dt is important in statistics. Show that the integral on the right converges for all real x ....
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