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

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1 EXAM 2 REVIEW 1. Determine the indefinite integral I = sin 6 (3 x ) dx . 2. Determine the indefinite integral I = 9 e 6 t - e 12 t dt . 3. Evaluate the definite integral I = π/ 3 π/ 4 ln(tan x ) sin x cos x dx . 4. Determine the indefinite integral I = 3 x 2 - 2 x 2 - 2 x - 8 dx . 5. Determine the indefinite integral I = 1 x + 1 + x dx . 6. Evaluate the definite integral I = π/ 4 0 tan 3 x sec 4 x dx . 7. Find the volume of the solid generated by revolving the region bounded by the graphs of y = 3 ln x, y = 0 , x = 4 e about the x -axis. 8. Evaluate the definite integral I = 3 3 / 2 0 x 3 (4 x 2 + 9) 3 / 2 dx . 9. *(If you can’t do this one, you should at least be able to do the next one.) Evaluate the definite integral I = 7 3 sin - 1 7 + 6 x - x 2 4 dx . 10. Determine the indefinite integral I = θ cos θ dθ . 11. Determine the indefinite integral I = t + 9 t dt . 12. Determine if the improper integral I = 9 1 1 3 x - 9 dx converges, and if it does, compute its value.
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2 13. Determine if the improper integral I = 1 ln x x 2 dx converges, and if it does, compute its value. 14. Determine if the improper integral
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