A community for students.
Here's the question you clicked on:
 0 viewing
MarcLeclair
 2 years ago
How does the integral sin5x = 1/5cos5x. I just do not understand where the 1/5 comes from x.x
MarcLeclair
 2 years ago
How does the integral sin5x = 1/5cos5x. I just do not understand where the 1/5 comes from x.x

This Question is Closed

ghazi
 2 years 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
 2 years 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
 2 years 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

SithsAndGiggles
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0ahhh the substitution rule makes sense x.x stupid me. THanks!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.