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swin2013

Integration by substitution

  • one year ago
  • one year ago

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  1. amoodarya
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    where is question?

    • one year ago
  2. swin2013
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    general integral with the function sin(2x) dx My work: u = 2x du/dx = 2 du = 2dx 1/2 integral (2sin(2x)dx) 1/2 integral (sinu * du) 1/2sin(2x) + C but that's not right i believe.. lol

    • one year ago
  3. swin2013
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    is it supposed to be cos instead of sin?

    • one year ago
  4. Spacelimbus
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    keep your derivatives in mind, what happens if you derive -cos(x)?

    • one year ago
  5. swin2013
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    sin

    • one year ago
  6. Spacelimbus
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    exactly.

    • one year ago
  7. swin2013
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    oh i just checked the answer sheet -_- it says cos...

    • one year ago
  8. swin2013
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    1/2 (cos(2x)) + C

    • one year ago
  9. Spacelimbus
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    hmm, well that's not the answer in my opinion, because if you derive that you get: \[\Large - \frac{1}{2} \sin(2x) \cdot 2 = - \sin(2x) \]

    • one year ago
  10. swin2013
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    oh... i didn't get that at all. idk, the given answer is 1/2cos(2x) + C

    • one year ago
  11. swin2013
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    is my u sub wrong?

    • one year ago
  12. Spacelimbus
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    No your substitution is perfect, it's more the way you integrated, you kept the sin function, which shouldn't be the case when you integrate, because when you differentiate you want to obtain the integrand again \[F(x)\prime =f(x) \]

    • one year ago
  13. swin2013
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    OHHHHHH snap I get it! lol

    • one year ago
  14. tkhunny
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    Seriously? Why would you EVER use substitution for a mere constant? It's just craziness. Speculate \(\int \sin(2x)\;dx = -\cos(2x)\;+\;C\) Check \(\dfrac{d}{dx}(-\cos(2x)) = 2\cdot \sin(2x)\) -- Oops, we missed a constant. Solve \(\int \sin(2x)\;dx = -\dfrac{1}{2}\cos(2x)\;+\;C\) -- Done. On the other hand: \(\int \sin(2x)\;dx = \int 2\sin(x)\cos(x)\;dx\) -- Now, THERE'S a candidate for Substitution.

    • one year ago
  15. swin2013
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    because I've been doing exponential functions all day -_- so i kept that in mind that i shouldn't change it. But just to make sure... i should integrate the function after i derive the u correct?

    • one year ago
  16. swin2013
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    oh the constant part i have no prob with hahaha general integrals = add or subtract c lol

    • one year ago
  17. tkhunny
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    I wish I could tell what "derive" means. I have not found it acceptable to use it as the verb form for finding a derivative.

    • one year ago
  18. swin2013
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    i'm not sure if that is sarcasm because i was tempted to give you the definition lolll but thanks!

    • one year ago
  19. tkhunny
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    No, not sarcasm, just discouragement. I don't recommend that usage. It just isn't generally in use.

    • one year ago
  20. swin2013
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    oh here it is. as long as we know the answer and the concept, it's all good.

    • one year ago
  21. Spacelimbus
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    exactly.

    • one year ago
  22. tkhunny
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    And perhaps that we managed to learn something else along the way. Good work.

    • one year ago
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