Pre-Calc Homework Solutions 254

Pre-Calc Homework Solutions 254 - 254 Section 6.3 e 2x 2e...

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Unformatted text preview: 254 Section 6.3 e 2x 2e 2x dx dv v cos 3x dx 17. Let u du e 2x cos 3x dx 1 sin 3x 3 1 1 (e 2x) sin 3x sin 3x (2e2x dx) 3 3 1 2x 2 2x e sin 3x e sin 3x dx 3 3 Let u du e2x 2e 2x dx dv v sin 3x dx 1 cos 3x 3 2 2x (e ) 3 1 2x 1 1 e sin 3x cos 3x cos 3x (2e 2x dx) 3 3 3 1 2x 4 2x e (3 sin 3x 2cos 3x) e cos 3x dx 9 9 13 2x 1 2x e cos 3x dx e (3 sin 3x 2 cos 3x) 9 9 1 2x e 2x cos 3x dx e (3 sin 3x 2 cos 3x) 13 3 1 2x 3 e 2x cos 3x dx e (3 sin 3x 2 cos 3x) 13 2 2 e 2x cos 3x dx 1 6 [e (3 sin 9 13 1 6 [e (2 cos 9 13 2 cos 9) 3 sin 9) e e 4 4 (3 sin ( 6) 2 cos ( 6)] (2 cos 6 3 sin 6)] 18.186 Check: NINT(e 2x cos 3x, x, 18. Let u du e 2x 2, 3) 18.186 e 2x dv 2x sin 2x dx 1 cos 2x 2 1 cos 2x ( 2e 2x dx) 2 2e dx 2x v ) sin 2x dx (e 1 cos 2x 2 1 2x e cos 2x 2 e 2x cos 2x dx Let u du e 2x dv 2x cos 2x dx 1 sin 2x 2 2e v e 2x sin 2x dx 1 2x e cos 2x 2 1 2x e (cos 2x 2 (e 2x ) sin 2x e C C 2 3 2x 1 2 1 sin 2x ( 2e 2x dx) 2 sin 2x) sin 2x) sin 2x) sin 2x) sin 4) sin 4) sin 2x dx 2 e e 2 2x sin 2x dx e 1 2x e (cos 2x 2 2x 2x sin 2x dx 2x 4 e (cos 2x 2x e 3 sin 2x dx 4 e 4 e 4 4 4 (cos 2x (cos 4 (cos 4 e6 [cos ( 6) 4 e6 (cos 6 4 sin ( 6)] sin 6) 125.028 Check: NINT(e 2x sin 2x, x, 3, 2) 125.028 ...
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