Question

Find the average value of the function on the given interval
f(x)=cos x; interval \[[\frac{ -\pi }{ 2 },\frac{ \pi }{2 }]\]

Answer 1

well the average value of f from -pi/2 to pi/2 is the integral \[\frac{ 1 }{ \Pi } \times \int\limits_{\frac{ -\Pi }{ 2 }}^{\frac{ \Pi }{ 2 }} \cos x dx = \frac{ 1 }{ \Pi } \times \sin x |_{\frac{ -\Pi }{ 2 }}^{\frac{ \Pi }{ 2 }}\]

Answer 2

is it \[\frac{ 1 }{\pi}*(\sin \frac{ \pi }{ 2 }-\sin \frac{ -\pi }{ 2 })\] which would simplify down to \[\frac{ 2 }{ \pi } \]

Answer 3

yes it's \[\frac{ 2 }{ π }\]

Answer 4

nice and I found it properly correct? It wasn't just luck that it came out that way?

Answer 5

yes, your result is accurate.

Answer 6

thnx a bunch. well earned medal