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# C4 integration short question watch

1. Whats the integral of sin(x)sin(x/2)
i think it has something to do with sin2x=2sinxcosx but cant figure it out
2. I could be mistaken (my C4 isn't great) but I think it's: 4/3(sin(x/2))^3

Differentiated would be 4 * 1/2 * cos(x/2) * sin^2(x/2)
= 2cos(x/2)sin^2(x/2)
=2sin(x/2)cos(x/2)sin(x/2)
=sin(x)sin(x/2)

I know my explanation is in reverse, but I hope this helps!
3. (Original post by mlyke)
Whats the integral of sin(x)sin(x/2)
i think it has something to do with sin2x=2sinxcosx but cant figure it out
Notice that from your identity you get so your integral turns into at which point you can just use
4. (Original post by thesporkthief)
I could be mistaken (my C4 isn't great) but I think it's: 4/3(sin(x/2))^3

Differentiated would be 4 * 1/2 * cos(x/2) * sin^2(x/2)
= 2cos(x/2)sin^2(x/2)
=2sin(x/2)cos(x/2)sin(x/2)
=sin(x)sin(x/2)

I know my explanation is in reverse, but I hope this helps!
I think that was the right answer but can you explain how u go from
=2sin(x/2)cos(x/2)sin(x/2) to
=sin(x)sin(x/2)

thanks
5. (Original post by RDKGames)
Notice that from your identity you get so your integral turns into at which point you can just use
ooh i understand now, thats pretty stupid of me thanks a lot

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