anonymous
  • anonymous
Integral(e^(ab))da= e^(ab)*b^-1 Why?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
As, going the other way: if I differentiate the right equation with respect to a, b doesn't dissapear, as it is a constant, then why does a b^-1 materialise in the antiderivative?
amistre64
  • amistre64
i take it thats a partial and not b(a)?
amistre64
  • amistre64
\[D_a(exp({ab}))=exp(ab)*(ab)'\] \[D_a(exp({ab}))=exp(ab)(a'b+ab')\] or maybe if bs a constant \[D_a(exp({ab}))=exp(ab)*b\]

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amistre64
  • amistre64
we need the 1/b to catch it; 1/b * b = 1
amistre64
  • amistre64
in other words, if we dont put something there to catch the "b" that flies out we dont get the derivative we are looking for
amistre64
  • amistre64
Dx is a way to notate a derivative operation on something.
amistre64
  • amistre64
Da means take the derivative of this stuff with respect to a
amistre64
  • amistre64
go ahead and replace b with your favorite constant thats not 0
amistre64
  • amistre64
youll see that if we dont have a 1/2 in the antiderivative that we end up with : exp(2a)*2 which is NOT what we are trying to undo.
amistre64
  • amistre64
so we apply a useful form of 1 into the antiderivative to help us out; since 1* anything doesnt change its value; we need a "2", or a "b" as the case may be, so lets use 2/2 and just pull out the 1/2 for later
anonymous
  • anonymous
Thanks, after writing that out it clicked.
amistre64
  • amistre64
:) youre welcome

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