Pre-Calc Homework Solutions 233

Pre-Calc Homework Solutions 233 - Section 6.1 9. 1 x 3 233...

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Unformatted text preview: Section 6.1 9. 1 x 3 233 6. dx ln x 3 C Check: d [ln x dx 3 6x C] 3) dx 1 x x6 6 x 2 3 [0.01, 5] by [ 3, 3] By setting the left endpoint at x 0.01 instead of x 0, 7. (x 5 8. ( x 9. e t/2 3x 2 2 3x x2 2 2 C x C we avoid an error that occurs when our calculator attempts 1 to calculate NINT , x, 1, 0 . The graph appears to be the x 3 x 5 t2 1) dx dt (e t/2 2e t/2 same as the graph of y 10. ln x. 5t 5t 5 t 1 ) dt C 2e 10. [ 5, 0.01] by [ 3, 3] t/2 C C 4 3 t dt 3 4 1/3 t dt 3 t 4/3 11. 0.01 instead of x 0, x3 1 dx x3 (x 3 x 4 x4 4 4 x 3) dx x 2 By setting the right endpoint at x we avoid an error that occurs when our calculator attempts to calculate NINT 1 , x, x 2 1 2x 2 C C x 1/3 1, 0 . The graph appears to be 12. ln ( x). 3 x 1 3 dx x (x 1/3 3 4/3 x 4 ) dx C the same as the graph of y 3 2/3 x 2 Section 6.1 Exercises 1. (x 2 2x 1) dx x3 3 13. x 2 x C 1 2/3 x dx 3 x 1/3 C 3 cos x x C 1 dx 2x Check: d x dx 3 3 14. (3 sin x x2 4 sin 3x) dx x dx sin 2 sec t 2 ln x e 2x cos 3x 3 C x x C 3 x2 C 2x 1 15. 2 cos 2 2 C 2. ( 3x Check: d (x 3 dx ) dx 16. 2 sec t tan t dt 17. 2 x 1 x 2 1 1 x dx ln x C C) 4 x) dx 3x 4 18. (x 2 sin 5x 2 3. (x 2 4x 1/2 ) dx x3 3 8 3/2 x 3 C ln x Check: d x3 dx 3 8 3/2 x 3 cos 5x 5 e 2 C 19. 5 sec 2 5r dr C x 2 tan 5r cot 7t 7 1 C C 4x 1/2 x 2 x 20. csc 2 7t dt 4. (8 csc x cot x) dx 8x csc x C 21. cos2 x dx Check: d (8x dx csc x 1 4x e 4 C) C 8 csc x cot x cos 2x dx 2 1 cos 2x dx 2 2 sin 2x x C 4 2 1 1 2 cos 2x dx 2 cos 2x dx 2 5. e 4x dx Check: d 1 4x e dx 4 22. sin 2 x dx e 4x 23. tan 2 d C x 2 sin 2x 4 C C (sec 2 1) d tan ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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