- Prove the following for all
with
:
- Prove the following formulas for
with
:
and,
- Proof. Here we compute, using the expansion/contraction of the interval of integration to get rid of the
And,
- Proof. Here we have a bunch of computations using part (a) and the formulas for sine and cosine of a sum:
where we know
and
since
.
Next,Then,
And for the fourth integral formula,
Finally,
I think that in the first two integrals of proof b (first line of math) you should have Sin[m x] Cos[n x]