408L_rev2 - 1 EXAM 2 REVIEW 1 Determine the indefinite...

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Unformatted text preview: 1 EXAM 2 REVIEW 1. Determine the indefinite integral I = sin6 (3x) dx. 9e6t − e12t dt. 2. Determine the indefinite integral I = π /3 3. Evaluate the definite integral I = π/4 ln(tan x) dx. sin x cos x 4. Determine the indefinite integral I = 3x2 − 2 dx. x2 − 2x − 8 5. Determine the indefinite integral I = √ 1 √ dx. x+1+ x π /4 tan3 x sec4 x dx. 6. Evaluate the definite integral I = 0 7. Find the volume of the solid generated by revolving the region bounded by the graphs of y = 3 ln x, y = 0, x = 4e about the x-axis. √ 3 3/2 8. Evaluate the definite integral I = 0 x3 dx. (4x2 + 9)3/2 9. *(If you can’t do this one, you should at least be able to do the next √ 7 7 + 6x − x2 −1 one.) Evaluate the definite integral I = dx. sin 4 3 10. Determine the indefinite integral I = θ cos θ dθ. √ 11. Determine the indefinite integral I = t+9 dt. t 9 12. Determine if the improper integral I = 1 √ 3 converges, and if it does, compute its value. 1 dx x−9 2 ∞ 13. Determine if the improper integral I = 1 ln x dx x2 converges, and if it does, compute its value. 4 1 dx 2 0 (x − 1) converges, and if it does, compute its value. 14. Determine if the improper integral I = ∞ 15. Determine if the improper integral I = 3 x2 e−x dx −∞ converges, and if it does, compute its value. 16. Find all first and second derivatives of f (x, y ) = ln(3x + 5y ). √ 17. Find the first partial derivatives of g (x, t) = arctan(x t). ex/y dA, 18. Calculate the iterated integral I = where D = {1 ≤ y ≤ 2, y ≤ x ≤ y 3 }. D 1 19. Calculate the iterated integral I = 0 1 √ x3 + 1 dx dy . y 20. Find the volume of the solid under the graph of z = 2x + y 2 and above the region enclosed by the graphs of x = y 2 and x = y 3 . 2 ln x 21. Reverse the order of integration in the integral but do not attempt to evaluate either integral. f (x, y ) dy dx, 1 0 ...
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This note was uploaded on 11/10/2011 for the course HDF 304 taught by Professor Gray during the Spring '08 term at University of Texas.

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408L_rev2 - 1 EXAM 2 REVIEW 1 Determine the indefinite...

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