anonymous
  • anonymous
integrate
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
what have you considered?
anonymous
  • anonymous
|dw:1442184148009:dw|
amistre64
  • amistre64
what is the derivative of: e^(kx) with respect to x? for some constant k

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amistre64
  • amistre64
ok, so this derivative looks similar to what we have, it differs by a sign right? lets alter its appearance some; multiply it by (-1/-1)
amistre64
  • amistre64
\[\int\frac{-1}{-1}\frac14e^{-x/4}dx\] \[\int\frac{1}{-1}\frac{-1}4e^{-x/4}dx\] \[\frac{1} {-1}\int\frac{-1}4e^{-x/4}dx\] or simply \[-\int-\frac{1}4e^{-x/4}dx\]
amistre64
  • amistre64
we know an antiderivative of the integral so, we should certainly be able to use it for a solution
amistre64
  • amistre64
u-subbing is a valid process, but i find that training yourself to see the possibilities of where it comes from is more conducive with timed tests :)
amistre64
  • amistre64
|dw:1442184708371:dw|
amistre64
  • amistre64
|dw:1442184778575:dw|
anonymous
  • anonymous
Thank you so much @amistre64
amistre64
  • amistre64
good luck
anonymous
  • anonymous
put -x/4=t x=-4t dx=-4 dt \[I=\frac{ 1 }{ 4 }\int\limits e^t(-4~dt)=-e^t+c=-e ^{\frac{ -x }{ 4 }}+c\]

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