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swin2013

  • one year ago

Integration by substitution

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  1. amoodarya
    • one year ago
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    where is question?

  2. swin2013
    • one year ago
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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

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

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

  5. swin2013
    • one year ago
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    sin

  6. Spacelimbus
    • one year ago
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    exactly.

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

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

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

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

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

  12. Spacelimbus
    • one year ago
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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 \[F(x)\prime =f(x) \]

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

  14. tkhunny
    • one year ago
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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.

  15. swin2013
    • one year ago
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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?

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

  17. tkhunny
    • one year ago
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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.

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

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

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

  21. Spacelimbus
    • one year ago
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    exactly.

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

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