Getting Integrate to produce the simple analytic result

Questions
,
1

Integrate[Sin[1.5 M+a] Cos[1.5 M+b] Sin[1.5 M+b] , {M, 0, 4 Pi}] produces -1.22465 x 10^{-16}Cos[a-2.b]+1.22465 x 10^{-16}Cos[a+2.b]+0. Sin[a-2b] + 0.Sin[a+2.b].

But the integral is rigorously zero with rather trivial trigonometric integrations. One could interpret the result of Integrate as zero, but why does Mathematica not give the simple answser? Is there a way to use Integrate on this product to yield the rigporous analytic result? Simplify [%] does not eliminate the terms with zero factor.

2

Dear Stanton,

please try

Integrate[Sin[3/2 M + a] Cos[3/2 M + b] Sin[3/2 M + b], {M, 0, 4 Pi}]

Mathematica assume that 1.5 etc in your inpute are finite precision numbers.

Cheers,
M.

3

Oh, I forgot:

Integrate[
 Sin[SetPrecision[1.5, Infinity] M + a] Cos[
   SetPrecision[1.5, Infinity] M + b] Sin[
   SetPrecision[1.5 , Infinity] M + b], {M, 0, 4 Pi}]

would also work…