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swin2013
 3 years ago
Integration by substitution
swin2013
 3 years ago
Integration by substitution

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swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0general 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

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0is it supposed to be cos instead of sin?

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.0keep your derivatives in mind, what happens if you derive cos(x)?

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0oh i just checked the answer sheet _ it says cos...

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.0hmm, well that's not the answer in my opinion, because if you derive that you get: \[\Large  \frac{1}{2} \sin(2x) \cdot 2 =  \sin(2x) \]

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0oh... i didn't get that at all. idk, the given answer is 1/2cos(2x) + C

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.0No 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 \[F(x)\prime =f(x) \]

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0OHHHHHH snap I get it! lol

tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.0Seriously? 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.

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0because 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?

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0oh the constant part i have no prob with hahaha general integrals = add or subtract c lol

tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.0I wish I could tell what "derive" means. I have not found it acceptable to use it as the verb form for finding a derivative.

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0i'm not sure if that is sarcasm because i was tempted to give you the definition lolll but thanks!

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

swin2013
 3 years ago
Best ResponseYou've already chosen the best response.0oh here it is. as long as we know the answer and the concept, it's all good.

tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.0And perhaps that we managed to learn something else along the way. Good work.
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