3. In the second part of the lab we will need to find the average value of the induced voltage over one quarter-cycle. Look at the top right function, f (x). Since f (x = 0) = 1, f (x = 90) = 0 and the " function is linear, it's clear that the average value of this function between x = ' 0 and x = 90 is 0.5 OI 3 06 KL.\" I Things get tricker if the function f (x) is not linear. We will need to know the 21 average value of the bottom right function, cos x, between x = 0 and x = 90. 0 We can see that cosx decreases Iore slowly than the linear function. It is, on ' 2 3 \"x\" N ' " average, closer to 1 than to 0 between x = 0 and x = 90, so the average value '2 _ of cos x in this range of x should be greater than 0.5. Prove that the average value ' x) _ COS x of cos x yields a. \"Q n """"" \"-5 I fun/2 cos(x)dx 2 : (cos x) = T = = 0.637 ' I dx 7T n 0 0 10 20 an 40 an on m N N Show your work below. 3"