Pre-Calc Homework Solutions 282

Pre-Calc Homework Solutions 282 - 282 Chapter 6 Review e 3x...

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Unformatted text preview: 282 Chapter 6 Review e 3x 3e 3x dx e 3x 19. Let u du e 3x dv v cos x sin x dx cos x 3 cos x e 3x dx 22. dy dx dy dy sin x dx Integrate by parts again. Let u du e 3x 3x 3e 3x 9e 3x dx sin x dx sin x dx e e dv v 3x 3x cos x dx sin x 3e 3e 3x 3x y y y (1) cos x cos x sin x sin x 9e C 3x 1 2 x 1 2 x dx x 2 1 x dx x 1 x2 2 dx x2 1 3 x 2x x 1 C 3 1 2 1 C 1 3 x sin x dx 4 3 C C 1 1 3 x3 3 10 e e 3x sin x dx 1 [ e 3x cos x 3e 3x sin x] 10 3 sin x cos x 3x e C 10 10 C y 2x 1 x 1 3 Graphical support: 20. Let u du x 2e Let u du 3x x2 2x dx dx x dx dv v 1 2 3x x e 3 e 3x dx 1 3x e 3 2 e 3xx dx 3 [ 2, 2] by [ 10, 10] dv v e 3x dx 23. dy dt 1 t 1 t t 4 4 1 1 3x e 3 1 2 3x 2 1 1 x e xe 3x e 3x dx 3 3 3 3 1 2 3x 2 2 x e xe 3x e 3x dx 3 9 9 1 2 3x 2 2 x e xe 3x e 3x C 3 9 27 x2 2x 2 e 3x C 3 9 27 dy dy y C y dt 4 dt C C 2 2 ln t 2 ln (t 4 ln (1) 4) y( 3) Graphical Support: dy 21. dx x2 1 x 2 x2 dy 1 x dx 2 2 x dy 1 x dx 2 1 2 1 3 y x x x C 2 6 [ 4.5, 5] by [ 2, 5] 24. y(0) y x3 6 C x2 2 1 x 1 dy d csc 2 cot 2 csc 2 cot 2 d csc 2 cot 2 d 1 csc 2 C 2 1 C 1 2 3 2 1 csc 2 2 3 2 dy dy y y C 4 Graphical support: [ 4, 4] by [ 3, 3] y [0, 1.57] by [ 5, 3] ...
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