Integration (1 Viewer)

[cutemouse]

Hello,

here's a question that my teacher couldn't do.. could someone please do it? thanks

If n is a positive integer, find in terms of n the three possible values of


Thanks

 

[Drongoski]

Hello,

here's a question that my teacher couldn't do.. could someone please do it? thanks

If n is a positive integer, find in terms of n the three possible values of


Thanks

1/n, 0, -1/n

= 1/n (n of form: 4m+3, m integer)

= 0 (n of form 4m or 4m+2; i.e. any even no)

= -1/n (n of form: 4m+1)

 

[cutemouse]

Uhh, I don't understand what you did above... How did you get to that?

 

[shaon0]

I=(1/n){sin(n*pi)-sin(n*(pi/2))}
Every cycle of pi. sin(x)=0 and every cycle of pi/2. sin(x)=+-1.
Case 1:
sin(n*(pi/2))=1, given that sin(n*pi)=0
Thus, I=-(1/n)
Case 2:
sin(n*(pi/2))=-1, given that sin(n*pi)=0
Thus, I=(1/n)
Case 3:
n=0.
Thus I=0.