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# Test notes PHSX 207

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This 2 page Class Notes was uploaded by Val Miller on Wednesday August 17, 2016. The Class Notes belongs to PHSX 207 at Montana State University - Bozeman taught by Gregory Francis in Fall 2016. Since its upload, it has received 7 views. For similar materials see College Physics ll in Physics at Montana State University - Bozeman.

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Date Created: 08/17/16

Spring 2015 - M172 Review Session - Mar. 5/15, 2015 - EXAM II 1. Circle the appropriate choice of TRUE or FALSE. Z 1 TRUE FALSE: You could use x = 4sec▯ to evaluate p 2 dx x ▯ 4 TRUE FALSE: Using partial fraction decomposition,1 = Ax + B (1 + x)2 (1 + x) TRUE FALSE: The formula for determining area of a surface of revolution about the Z b p 0 x-axis is S = 2▯ f(x) 1 + f (x)dx Z 5 a ▯ 1 ▯1 ▯ ▯1 1 ▯5 TRUE FALSE: (x ▯ 3) dx = x ▯ 30 = 2 ▯ 3= 6 0 x TRUE FALSE: Using an appropriate triangle, if x = 3sin▯, then tan▯ = 2 9 ▯ x TRIG INTEGRALS / TRIG SUB 2. Evaluate each integral using trigonometric identities where appropriate Z Z Z ▯ (a) tan xsec xdx (c) tan xdx (e) (1 + sinx) dx 0 Z Z Z 3 p (b) cos xdx (d) sin8xsin5xdx (f) cos xdx 3. Evaluate each integral using trigonometric substitution where appropriate Z p Z 3 Z (a) x 3 1 ▯ x dx x (e) 1 dx (c) p 2 dx (4 + 9x )2 Z Z x + 100 Z 1 1 x + arcsinx (b) p 2 dx (d) 3p 2 dx (f) p 2 dx x + 16 x x ▯ 2 1 ▯ x PARTIAL FRACTIONS 4. Evaluate each integral using the methods of partial fraction decomposition where appropriate Z Z Z p 1 x + 9 x (a) x ▯ 1 dx (c) x(x + 9)dx (e) dx x ▯ 4 Z x ▯ 2x ▯ 4 Z 1 Z p (b) dx (d) dx (f) 1 + e dx x ▯ 2x 2 x + 4x + 5 IMPROPER INTEGRALS 5. Determine whether the improper integral converges, and if so evaluate it. Z Z Z ▯1 1 1 arctanx 1 ▯x (a) p dx (c) 2 dx (e) xe dx ▯1 2 ▯ x 0 1 + x 0 Z 1 Z 0 Z 2 1 3x 2 (b) (3x + 1)2dx (d) (x + 1)(x ▯ 2) (f) x lnxdx 1 ▯1 0 COMPARISON THEOREM Z 1 1 ▯ Example: Use the Comparison Theorem to determine whether or not the integral p 5 x ▯ 1 converges. p p 0 ▯ x ▯ 1 ▯ x p 1 ▯ p1 ▯ 0 x ▯ 1 x Since converges/diverges (circle one) because p = , converges/diverges (circle one) by the Comparison Theorem. 6. Use the Comparison Theorem to determine whether or not the integral converges. Z 1 Z 1 Z 1 x 2 jcosxj (a) x + x dx (b) p 3 dx (c) p3 dx 1 1 x ▯ 1 0 x APPLICATIONS 7. Find a constant C such that p(x) is a probability density function on the given interval, and compute the probability indicated. C (a) p(x) = 2 on [0;1); P(0 ▯ X ▯ 2) (2x + 1) Ce ▯x (b) p(x) = on (▯1;1); P(X ▯ ▯4) 1 + e2x 8. Calculate the arc length of the function over the given interval. (a) y = 3 + 4x=, [0;1] (b) y = ln(secx), [0;▯=3] (c) y =1x ▯ 1 lnx, [1;2e] 4 2 9. Compute the surface area of revolution about the x-axis over the given interval. 3 (a) y = x , [0;2] (b) y = p 1 + 4x, [1;5] 2 3=2 1 1=2 (c) y = x ▯ x , [1;2] 3 2 10. Calculate the uid force on the side of a right triangle of height 3 m and base 2 m submerged in water vertically, with its upper vertex at the surface of the water. ▯ 11. A plate is designed in the shape of the region under y = sinx for 02. Set up but do not integrate an integral to ▯nd the uid force on the plate if it is submerged in 1 meter of a uid of kg density 700m3.

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