Math2400
  • Math2400
evaluate the integral?
Mathematics
katieb
  • katieb
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Math2400
  • Math2400
\[\int\limits_{-1}^{1} \frac{ 3e ^{acrtan(y)} }{ 1+y^2 } dy\]
zepdrix
  • zepdrix
u - subbbbbb \c:/
zepdrix
  • zepdrix
remember your derivative of arctan(x)?

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zepdrix
  • zepdrix
\[\Large\rm \int\limits\limits_{-1}^{1} \frac{ 3e ^{acrtan(y)} }{ 1+y^2 } dy\quad =\quad3\int\limits_{-1}^{1}e^{\color{orangered}{\arctan(y)}}\left(\color{royalblue}{\frac{1}{1+y^2}dy}\right)\]
zepdrix
  • zepdrix
Rememberrrrrrr? <.<
Math2400
  • Math2400
mmmm i still didn't get it lol i tried u-sub tho. Let me post my work :)
Math2400
  • Math2400
never mind my phone is acting dumb >< but i tried to get wolfram alpha to help but it coduldnt calculate it
zepdrix
  • zepdrix
|dw:1433721955691:dw|So the derivative of arctan(x) is 1/(1+x^2)
zepdrix
  • zepdrix
\[\Large\rm 3\int\limits\limits_{-1}^{1}e^{\color{orangered}{\arctan(y)}}\left(\color{royalblue}{\frac{1}{1+y^2}dy}\right)=3\int\limits e^{\color{orangered}{u}}\left(\color{royalblue}{du}\right)\]
zepdrix
  • zepdrix
with new limits of integration of course :o

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