Solving the Integral of sin(1-x)sinx: A Step-by-Step Guide

[powerplayer]

Homework Statement

integral of sin(1-x)sinx dx

Homework Equations

The Attempt at a Solution

so i did by parts once and got -sinxcos(1-x) - integral of -cos(1-x)cosx dx

then i did by parts again and got -sinxcos(1-x) + cosxsin(1-x) - integral of -sin(1-x)sinx dx

if you take out the negative on the last integral you end up where you started? anyone know where i messed up?

 

[Whitishcube]

Instead of parts, you could try using a double angle formula on sin(1-x).

 

[powerplayer]

oh i think i see it i forgot to divide by the -1 each time i took the integral in the by parts

 

[powerplayer]

nevermind i still did not get the right answer how do i use double angle on sin(1-x_ i thought it had to be in the form sin2x?

 

[fzero]

Not quite the double angle formula, but rather the trig identity for sin of a sum.

 

[powerplayer]

i got it now thx