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yuki
 5 years ago
find the integral
yuki
 5 years ago
find the integral

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Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} e^x \sin(x) dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(1/2)[e(\sin1\cos1)+1\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0I was thinking of integration by parts

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0letting e^xdx = dv and u = sin(x)

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0that makes e^x = v and du = sin(x)dx

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0thus making uv vdu = e^x cos(x)  [int] e^x cos(x) dx

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0so now I need to figure out what \[\int\limits e^x \cos(x) dx\]

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0so using same stuff, I would get e^x sin(x)  [int] e^x sin(x) dx

Yuki
 5 years ago
Best ResponseYou've already chosen the best response.0since I get the same thing on both sides, I can add them on both sides, right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0u can use dis..the formula integral exp(alpha x) sin(beta x) dx = (exp(alpha x) (beta cos(beta x)+alpha sin(beta x)))/(alpha^2+beta^2):

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my idea is that sinx= Im(e^ix) so the integral is Im( e^(i+1)x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that is Im(e^i+1)x/(i+1)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now put back 1 and 0 (e^(i+1)1)/i+1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do you think guys?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am stuck here.. what is e^i+1?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yuki..u r right u can do by using by parts..see \[\int\limits_{0}^{x}e^xsin(x)dx=[e^xsin(x)]\int\limits_{0}^{x}e^xcos(x)dx=e^xsin(x)[e^xcos(x)+\int\limits_{0}^{x}e^xsin(x)dx]\] \[2\int\limits_{0}^{x}e^xsin(x)dx=e^xsin(x)e^xcos(x)\] Now Put x=1 in the above..:)
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