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 one year ago
How does the integral sin5x = 1/5cos5x. I just do not understand where the 1/5 comes from x.x
 one year ago
How does the integral sin5x = 1/5cos5x. I just do not understand where the 1/5 comes from x.x

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ghazi
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{b}^{a} \cos 5x= \frac{ 1 }{ 5 }\sin 5x (a \to b)\]

ghazi
 one year ago
Best ResponseYou've already chosen the best response.1just treat 5x as one thing and then use property of integration which says coefficient gets denominator so 5 comes underneath sin 5x

MarcLeclair
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I do know its like a chain rule ( so treat sin5x than 5x.). However when you have a coefficient (5x) i thought it would go as 5x = 5x ^2/2

ghazi
 one year ago
Best ResponseYou've already chosen the best response.1nope it wont go that way

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.2Use a substitution: \[u=5x\Rightarrow du=5\;dx\Rightarrow \frac{1}{5}du=dx\] In the integral, you have \[\int\sin(5x)\;dx=\int\sin(u)\;\left(\frac{1}{5}\;du\right)=\frac{1}{5}\int\sin(u)\;du\] which is equal to \[\frac{1}{5}\cos(u)+C=\frac{1}{5}\cos(5x)+C\]

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.2In short, the 1/5 comes from the substitution for dx, which depends on the sub you make for 5x.

MarcLeclair
 one year ago
Best ResponseYou've already chosen the best response.0ahhh the substitution rule makes sense x.x stupid me. THanks!
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