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Brooke_army
 2 years ago
Integration by parts
Brooke_army
 2 years ago
Integration by parts

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Brooke_army
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{} \cos(10x)dx\] u=10x

Mimi_x3
 2 years ago
Best ResponseYou've already chosen the best response.3\[\int\limits cosaxdx =\frac{1}{a} sinax+c\]

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0just use the basic formula : int (cosAx) dx = 1/A * sinAx + c

Brooke_army
 2 years ago
Best ResponseYou've already chosen the best response.0I don't understand the basic formula

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2@Brooke_army "parts" is something else that you may not have seen yet. this type of integration is usually called "u  substitution"

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2if you didn't have the \(10x\) you would have \[\int cos(x)dx=\sin(x)\] because \[\frac{d}{dx}[\sin(x)]=\cos(x)\] but \[\frac{d}{dx}[\sin(10x)]=10\cos(10x)\] by the chain rule therefore, to get what you want, you have to divide by \(10\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2so if you take the derivative of \(\frac{1}{10}\sin(10x)\) you get exactly what you want, namely \(\cos(10x)\)
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