I still don't know the math symbols, so please bear with me!
I have the big S thing over sin(2X)*DX, its antidifferentiation is -(cos(2X))/2 + C
I have completely lost where that over 2 comes from. Wolfram alpha is not helpful. I realize that somewhere we pull a 1/2 out in front of everything, but I don't know where.
Thanks, I hope I'm making SOME sense.
Okay Skeeter, I went back over this and there are two steps in particular that have me. When the 1/2 shows up in front of everything, how did it get there and why?
My instructor has taken a completely different approach to this than my book did, hers is an easier way but I think I've managed to drop something somewhere.
When you are substituting into , you have to substitute for every "x", even the one is "dx".
As skeeter said, he let u= 2x. Differentiating both sides of that, du= 2 dx.
There are two ways of thinking about that but they give the same result:
1) Multiply and divide the integral by 2-
so your integral becomes .
2) Divide both sides of du= 2 dx by 2 to get and replace dx by that-
Notice that it is the fact that " " is a constant that allows us to move it in or out of the integral at will.