Question

Find the average value of the function on the given interval. F(theta)=sec^2(theta/2), [0, pi/2]

Answer 1

\[\frac{\sec^2(\frac{\pi}{4})-\sec^2(0)}{\frac{\pi}{2}-0}\] is a start
then you have to compute

Answer 2

oh unless this means "mean value" in which case you have to integrate

Answer 3

Nope it just says the average value.

Answer 4

are you doing integral calculus?

Answer 5

yep

Answer 6

\(\sec(\frac{\pi}{4})=\sqrt{2}\) and \(\sec(0)=1\) so you would get
\[\frac{2-1}{\frac{\pi}{2}}=\frac{2}{\pi}\]

Answer 7

or if this is mean value you would get
\[\frac{2}{\pi}\int_0^{\frac{\pi}{2}}\sec^2(\frac{x}{2})dx\]

Answer 8

anti derivative of secant squared is tangent, so it should be easy to complete