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swin2013

  • 2 years ago

Integration by substitution

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  1. amoodarya
    • 2 years ago
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    where is question?

  2. swin2013
    • 2 years 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
    • 2 years ago
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    is it supposed to be cos instead of sin?

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

  5. swin2013
    • 2 years ago
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    sin

  6. Spacelimbus
    • 2 years ago
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    exactly.

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

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

  9. Spacelimbus
    • 2 years 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
    • 2 years ago
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    oh... i didn't get that at all. idk, the given answer is 1/2cos(2x) + C

  11. swin2013
    • 2 years ago
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    is my u sub wrong?

  12. Spacelimbus
    • 2 years 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
    • 2 years ago
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    OHHHHHH snap I get it! lol

  14. tkhunny
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    oh the constant part i have no prob with hahaha general integrals = add or subtract c lol

  17. tkhunny
    • 2 years 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
    • 2 years 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
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    exactly.

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

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