A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Average value of a function on an interval.
Will post equstion and work in a comment
anonymous
 one year ago
Average value of a function on an interval. Will post equstion and work in a comment

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ \pi  0 } \int\limits\limits_{0}^{\pi} \sin (x) dx\] \[\int\limits_{0}^{\pi} \sin(x) dx = [\cos] _{0}^{\pi}\] \[[\cos \pi]  [\cos 0] => [(1)]  [1] = 1 + 1 = 2\] Average value = \[\frac{ 1 }{ \pi } (2) = \frac{ 2 }{ \pi }\] I'm asked to find the x value that corresponds to 2/pi sin(x) = 2/pi using the arcsin on the calculator I get ~ 0.690 But there is a second x value that corresponds to 2/pi, which is 2.451, how do I solve for the 2nd x value?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can I find the 2nd x value algebraically, using calculus, or using a graphing calculator?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0it's going to be symmetrical about \(\pi/2\)dw:1443181191167:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@IrishBoy123 Thank you. How do I calculate it?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443192745454:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443192978309:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. This is what I did. Please let me know if I over complicated it, or if there's a simpler way. Since the interval is [0, pi] and the first coordinate is 0 + arcsin(2/pi) the second coordinate is pi  arcsin(2/pi) = 2.451

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@IrishBoy123 How did you calculate it?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0the calculator gives you the first answer, but you know from the curve that there are two. the symmetry of the sine curve gives you the second, which was what i was getting at with this: dw:1443210395870:dw but from knowing \(\sin(\pi  x) = \sin \pi \cos x  \sin x \cos \pi = \sin x\) you migt hav egot a result from another direction but i saw the symmetry of the curve....if that answers your question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I get the symmetry of the sine curve. I don't understand sin(π−x)=sinπcosx−sinxcosπ=sinx

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0second part was just saying/showing that \(sin (\pi  x) = \sin x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thanks for your help
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.