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anonymous
 one year ago
Find the average value of f(x) = sin(x) over the interval [0, π].
anonymous
 one year ago
Find the average value of f(x) = sin(x) over the interval [0, π].

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Average value (A) of a function f(x) over the interval from x = a to x = b \[\Large A = \frac{1}{ba} \int_{a}^{b} f(x) dx\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1In your case, you have a = 0 b = pi f(x) = sin(x) \[\Large A = \frac{1}{ba} \int_{a}^{b} f(x) dx\] \[\Large A = \frac{1}{\pi0} \int_{0}^{\pi} \sin(x) dx\] \[\Large A = \frac{1}{\pi} \int_{0}^{\pi} \sin(x) dx\] \[\Large A = ???\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what's the integral of sin(x) ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes cos(x) + C we can drop the +C because we have a definite integral

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1evaluate cos(x) when x = pi evaluate cos(x) when x = 0 subtract the results to get ???

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got pi over 2 but someone told me just 2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah the integral portion should evaluate to 2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1which is why A = 2/pi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay thank you very much for clearing that up
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