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

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

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

MarcLeclairBest ResponseYou've already chosen the best response.0
Yeah 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
 one year ago

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

SithsAndGigglesBest ResponseYou've already chosen the best response.2
Use 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 \[\frac{1}{5}\cos(u)+C=\frac{1}{5}\cos(5x)+C\]
 one year ago

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

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