Hi, I just registered. I am a bit stucked at an example exercise. When I work out the integral (bottom of the picture) I get -V/jnπ. The two zero-limits of the integrals give both -V/jnπ , the other limits should give -2sin(nπ)/jnπ which always is zero.

Because the resolution of the above picture is a bit low I link to an extra picture.

I always assume at first that I make a mistake when I get a different result but I can't find any mistake.


@Moderators: I guess it would be better if the title would be: electronic circuits - error in book or my error?

 

The book answer given is correct. We can't begin to point out where you made your mistake unless you show us your work.

 

My attempt.

An earlier example in the book:

 

Your working is correct thus far. Try evaluating your result at any odd value of n and your answer will agree with the book result.

 

You're doing fine. You just need to finish things.

You could massage things to replace the complex exponentials with a trig formula, or you could just take note of the fact that 'n' has to be an integer and consider what the results are when n is even and when n is odd.

You're very close.

 

I think I understand it.
When n is odd you get -1 for e^j*n*pi = cos(n*pi) + j*sin(n*pi) because cos(n*pi) = -1 and sin(n*pi) = 0 for n is odd. The same for e^-j*n*pi = cos(-n*pi) + j*sin(-n*pi).

 

Yep, that'll do for when n is odd.

Be sure you do the same thing for n even to see that those terms vanish.

 

I did. Thanks.