00:01
According to the question we have to find the average value of cos t on the interval 0 to pi, 0 to pi by 2, 0 to pi by 4 and interval 0 to 0 .01.
00:26
The formula for average value is 1 upon b minus a integration a to b f t.
00:49
Therefore, for interval 0 to pi, a equals to 0, b equals to pi and f t equals to cos t.
01:02
On putting the values we have 1 upon pi minus 0 integration 0 to pi cos t dt.
01:12
This implies 1 upon pi.
01:14
Since integration of cos t is sin t and the limiting value is 0 to pi.
01:21
On putting the limiting value we have 1 upon pi sin pi minus sin 0.
01:28
Since the value of sin pi is 0 and the value of sin 0 is also 0.
01:33
Therefore, this is equals to 0.
01:36
Therefore, for interval 0 to pi the value of 1 upon pi minus 0 integration 0 to pi cos t dt is equals to 0.
01:55
Now for interval 0 to pi by 2, a equals to 0, b equals to pi by 2 and f t equals to cos t.
02:08
Therefore, the value of 1 upon b minus a integration a to b f t dt is equals to 1 upon pi by 2 minus 0 integration 0 to pi by 2 cos t dt.
02:26
This is equals to 2 upon pi sin t limit 0 to pi by 2.
02:34
This is equals to 2 upon pi sin pi by 2 minus sin 0.
02:42
The value of sin pi by 2 is 1 and the value of sin 0 is 0...