Can anyone help with the following integral:
int[sqrt(2/L)*sin((n*Pi*x)/L)]dL
The hint given is to use the trig identity:
sin(alpha)*sin(beta) = (1/2)*cos(alpha - beta) - (1/2)*cos(alpha + beta)
Thanks.
Hello, Ideasman!
If no one is responding, it's that the problem makes no sense.
. . I did an autopsy and came up with a COD . . .
int[sqrt(2/L)*sin((n*Pi*x)/L)]dL . ??
The hint given is to use the trig identity:
. .
Could this be the problem?
. .
. . . . . . . . . . . . . . . . .
Apply the identity:
. .
The problem becomes:
. .
Then use substitution: . and
It's a good thought. I came up with something similar, but I think we would have to leave the integral as "dL" otherwise the first sin function is simply a constant and we wouldn't need the hint. In fact, the integral becomes rather trivial. The problem I had with this is if we are integrating over L then I can't find a way to do the integral, and I suspect it has no closed form. (If I remember correctly anyway.)
But you are definitely right about one thing: this problem makes no sense as it is stated.
-Dan