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appleduardo Group Title

what is the integral of e^(senx) 4cosx dx ? how can i solve it?

  • one year ago
  • one year ago

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  1. appleduardo Group Title
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    \[\int\limits_{}^{}e ^{sen x} 4\cos x dx\]

    • one year ago
  2. geerky42 Group Title
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    sen? You mean sec?

    • one year ago
  3. satellite73 Group Title
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    try \(u=\sin(x), du=\cos(x)dx\) and you get it in one step

    • one year ago
  4. appleduardo Group Title
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    i got \[[e^{sen x} +c] [4 sen x + c]\] is that correct?

    • one year ago
  5. appleduardo Group Title
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    i meant "sin":

    • one year ago
  6. tkhunny Group Title
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    \(\int e^{\sin(x)}\cdot 4\cos(x)\;dx\) Following satellite73 suggestion u = sin(x) du = cos(x)dx This gives \(\int e^{u}\cdot 4\;du = 4\cdot e^{u} + C\) Substitute back to where we started. \(4\cdot e^{\sin(x)} + C\) Be careful, consistent, and confident.

    • one year ago
  7. appleduardo Group Title
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    thank you so much! but what happened with cos ?

    • one year ago
  8. tkhunny Group Title
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    It's all in there with the nature of the substitution. See the definition of du.

    • one year ago
  9. appleduardo Group Title
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    so in this case cos represents the derivative for sin in the formula , right?

    • one year ago
  10. tkhunny Group Title
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    That is where it came from. You can't just substitute a function. The nature of dx changes when you do that. Is English your first language? The answer to this question might help other folks understand where "sen(x)" came from.

    • one year ago
  11. appleduardo Group Title
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    haha yeah, uhmm but right now im studying in a spanish-speaking country, so sometimes (unconsciously) isay or write spanish :/ . thank you so!

    • one year ago
  12. tkhunny Group Title
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    No worries - as long as you don't mind freaking people out when you accidentally write the spanish versions of things. Good work!

    • one year ago
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