Posted by Anonymous on Thursday, February 9, 2012 at 7:00pm.
Calculate the average over the given interval. f(x)=sin(pi/x)/x^2, [1,2]

College Calculus  Steve, Thursday, February 9, 2012 at 9:23pm
Let u = 1/x
du = dx/x^2
Int(sin(pi/x)/x^2 dx)[1,2]
= Int(sin(pi*u) du)[1,.5]
= 1/pi cos(pi*u) [1,.5]
= 1/pi(cos pi/2  cos pi)
= 1/pi(0+1)
= 1/pi
Since the interval length is 1, the average is just 1/pi