Question

int between pi and -pi (sin5xcox3x)

Answer 1

\[\int\limits_{-\Pi}^{\Pi}\sin 5x \cos 3x\]

Answer 2

use trig identities for sin(u+v) and cos(u+v) and expand out to sin(x) and cos(x)

Answer 3

I understand the trig ident thus giving answer of -1/16 cos 8x -1/4 cos2x... but if its between pi and -pi isn't zero?

Answer 4

cos(x)=cos(-x)

Answer 5

cos pi and cos -pi
both equal -1 ?

Answer 6

so you have (1/16+1/4)*2

Answer 7

I have tried two different ways and get zero both ways.
yes, cos(PI)=cos(-PI)=-1. That is why on the interval (-PI,PI), it yields a zero.