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swin2013Best ResponseYou've already chosen the best response.0
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

swin2013Best ResponseYou've already chosen the best response.0
is it supposed to be cos instead of sin?
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.0
keep your derivatives in mind, what happens if you derive cos(x)?
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
oh i just checked the answer sheet _ it says cos...
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.0
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

swin2013Best ResponseYou've already chosen the best response.0
oh... i didn't get that at all. idk, the given answer is 1/2cos(2x) + C
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.0
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

swin2013Best ResponseYou've already chosen the best response.0
OHHHHHH snap I get it! lol
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.0
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

swin2013Best ResponseYou've already chosen the best response.0
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

swin2013Best ResponseYou've already chosen the best response.0
oh the constant part i have no prob with hahaha general integrals = add or subtract c lol
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.0
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

swin2013Best ResponseYou've already chosen the best response.0
i'm not sure if that is sarcasm because i was tempted to give you the definition lolll but thanks!
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.0
No, not sarcasm, just discouragement. I don't recommend that usage. It just isn't generally in use.
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
oh here it is. as long as we know the answer and the concept, it's all good.
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.0
And perhaps that we managed to learn something else along the way. Good work.
 one year ago
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