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Antiderivative of 6e^x and 4x^2

  1. May 24, 2010 #1
    antiderivative of 6e^x and 4x^2

    --> 6e^x
    -->1/6e^x??


    --> 4x^2
    --> 2x^3??
     
  2. jcsd
  3. May 24, 2010 #2
    Could you tell the steps you followed to find anti-derivative of [itex] 4x^2 [/itex] and how you got the answer.
     
  4. May 24, 2010 #3
    4x^2:
    One of the teachers said today to add one to the power, and divide whats out front by what the power was. So 4/2 = 2, and 2 + 1 = 3..
     
  5. May 24, 2010 #4
    Oh no! As far as adding one to the power is ok, but could you re-call correctly what has been told about the divisor.
    You can refer to standard integrals in the PF library to know the integration of [itex] x^n [/itex].
     
  6. May 24, 2010 #5
    Ok I think I figured it out. Thanks heaps for helping anyway. Don't know what my teacher was talking about but!! Still don't know the 6e^x one but..
     
  7. May 24, 2010 #6

    HallsofIvy

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    The derivative of Cf(x), where C is a constant, is Cf'(x) so [itex](6e^x)'= 6(e^x)'[/itex]. Do you know what the derivative of [itex]e^x[/itex] is?
     
  8. May 24, 2010 #7
    It's just itself. So the whole thing is just the same? It's still just 6e^x..?
     
  9. May 24, 2010 #8
    Yes. Remember what happens when you derive something with a constant in front of it? You pull the constant out:

    [tex]\frac{d}{dx} 6e^{x}[/tex]
    [tex]6\frac{d}{dx} e^{x}[/tex]
    [tex]6(e^{x})[/tex]

    The function exdoesn't change when you derive it unless you have something other than x in the exponent and have to use the chain rule.
     
  10. May 24, 2010 #9
    don't forget your constant of integration, but yes.
     
  11. May 24, 2010 #10
    My bad.

    [tex]\int{6e^{x}} dx =6\int{e^{x}} dx = 6e^{x} + c[/tex]
     
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