How to Solve an Equation with a Substitution Method?

  • Thread starter I dun get it
  • Start date
In summary, the conversation involves finding the value of an integral using a substitution method. The formula for this method is given as \int f(x) dx = F(x), where F(x) is the antiderivative of f(x). The integral from -1 to 3 is given as 12, and the goal is to find the integral from -1 to 1 by substituting u=2x+1. The relationship between dx and du is discussed, and the solution is found to be 6. The conversation ends with a playful comment about the user changing their username.
  • #1
I dun get it
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[PLAIN]http://img517.imageshack.us/img517/6328/q75c.gif

I know that you have to substitute u=2x+1 into the second equation, but I don't know where to go from there.
 
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  • #2
Let [tex] \int f(x) dx = F(x) [/tex]

then [tex] \int ^3_{-1} f(x) dx = F(3) - F(-1) = 12[/tex]

so [tex] \int^1_{-1} f(2x+1) dx = ? [/tex]
 
  • #3
Gregg said:
Let [tex] \int f(x) dx = F(x) [/tex]

then [tex] \int ^3_{-1} f(x) dx = F(3) - F(-1) = 12[/tex]

so [tex] \int^1_{-1} f(2x+1) dx = ? [/tex]

The answer given is 6, whereas that gives me 12.
 
  • #4
Try actually doing the substitution. If u=2x+1, what's the relation between dx and du?
 
  • #5
Oh, I get it now.
 
  • #6
I dun get it said:
Oh, I get it now.
So now you'll need to change your user name.:biggrin:
 

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