Beautiful Sunset Painting by Artist

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The discussion focuses on a mathematical substitution error in an integral involving the function e^-x. Participants clarify that the correct substitution should not include dx when defining u and emphasize the importance of properly substituting variables throughout the integral. One user acknowledges a careless mistake regarding the inclusion of dx but seeks confirmation on the rest of the work. The consensus is that aside from this error, the overall approach appears correct. The conversation highlights the significance of accurate variable substitution in calculus.
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http://img.photobucket.com/albums/v124/mugenlude99/myhw1.jpg

did i do this correct?

thanks
 
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There's something wrong, you shouldn't do u = e^-x dx, only u = e^-x and when you say -du = e^-x dx, you have to substitute it completely in the integral i mean -\int { tan(u)du}
 
Cyclovenom said:
There's something wrong, you shouldn't do u = e^-x dx, only u = e^-x and when you say -du = e^-x dx, you have to substitute it completely in the integral i mean -\int { tan(u)du}
i think i know what you're saying, but i took the -1 out since its a constant.

:confused:
 
that's ok, I'm talking about your substitution... You should not pick u = e^-x dx, why without dx? you will know why not later, and if you have a -du = e^-x dx, you should not have -\int {tanu dx} you should have -\int {tanu du} see what i mean?, remember in your du you have the dx.
 
Cyclovenom said:
that's ok, I'm talking about your substitution... You should not pick u = e^-x dx, why without dx? you will know why not later, and if you have a -du = e^-x dx, you should not have -\int {tanu dx} you should have -\int {tanu du} see what i mean?, remember in your du you have the dx.
oh sorry yeah that is a careless mistake, but other than the dx it's ok?
 
nomi said:
oh sorry yeah that is a careless mistake, but other than the dx it's ok?

Aside from that it looks good to me.
 
NateTG said:
Aside from that it looks good to me.
ok thanks a lot guys :)
 
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