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anonymous

  • 4 years ago

integrate s4^s ds

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  1. dumbcow
    • 4 years ago
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    \[\large \int\limits_{}^{}s*4^{s} ds\]

  2. anonymous
    • 4 years ago
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    i think it is integration by parts u =s, dv= 4^s ds, du = ds, but what is v

  3. dumbcow
    • 4 years ago
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    4^s / ln(4) \[\int\limits_{}^{}a^{x} = \frac{a^{x}}{\ln(a)}\]

  4. dumbcow
    • 4 years ago
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    yes you're right to use integration by parts

  5. anonymous
    • 4 years ago
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    final answer is 4^s/ln4(s-1/ln4)+c

  6. anonymous
    • 4 years ago
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    thanks, im doing web assign right now, and i keep getting stuck

  7. dumbcow
    • 4 years ago
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    hmm i get something a little different: \[\large \frac{s*4^{s}}{\ln(4)} -\frac{4^{s}}{(\ln(4))^{2}}\]

  8. anonymous
    • 4 years ago
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    that is the same, mine is just simplified, i took out the s/ln4

  9. anonymous
    • 4 years ago
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    how do you draw your equations so nice?

  10. anonymous
    • 4 years ago
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    how to integrate e^(−θ) cos 4θ dθ

  11. dumbcow
    • 4 years ago
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    oh i see, i didn't read your answer right use the equation button, frac{}{} allows you to write nice fractions

  12. dumbcow
    • 4 years ago
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    to write exponents....x^{ }

  13. anonymous
    • 4 years ago
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    \[e^{-\theta} cos4\theta d\theta\]

  14. dumbcow
    • 4 years ago
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    integration by parts again...here you will have to do it twice u = e^-x , dv = cos 4x du = -e^-x, v = 1/4 sin4x

  15. dumbcow
    • 4 years ago
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    The 2nd time should look like this: u = e^-x , dv = sin 4x du = -e^-x, v = -1/4 cos 4x

  16. dumbcow
    • 4 years ago
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    resulting in: \[\int\limits_{}^{}e^{-x}\cos(4x) = \frac{1}{4}e^{-x}\sin(4x)-\frac{1}{16}e^{-x}\cos(4x)-\frac{1}{16}\int\limits_{}^{}e^{-x}\cos(4x)\]

  17. dumbcow
    • 4 years ago
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    then notice the integrals are exactly the same, so think combining like terms add 1/16 integral to other side then all you have to do is divide by a constant

  18. dumbcow
    • 4 years ago
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    do you follow?

  19. anonymous
    • 4 years ago
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    ? maybe, but the answer cannot contain an integral

  20. dumbcow
    • 4 years ago
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    thats right, so imagine you treat the integrals like variables and combine like terms move it over to other side where the original integral is

  21. anonymous
    • 4 years ago
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    awesome, thanks!

  22. dumbcow
    • 4 years ago
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    your welcome here is a great resource for checking your work http://www.wolframalpha.com/input/?i=integrate+e%5E-x+*+cos%284x%29+dx

  23. anonymous
    • 4 years ago
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    I appreciate your help, I hope you have a wonderful day

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