Find the definite integral using the Fundamental Theorem of Calculus.

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Find the definite integral using the Fundamental Theorem of Calculus.

Mathematics
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\[\int\limits_{-1}^{1} e^-x (4-e^x) dx\]
see the thing is iruno how to break this ice
is exactly what i need help with

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Other answers:

That's e^(-x) by the way And I know, I'm so lost.
haha yeh this crap makes people lost in formulas man
so define the fundamental thrm of calculus; then see how that applies :)
My real question is, I don't know where to start with this problem.
start by defining the FTC and see how it applies lol.... that is the start
That does nothing for me.
expand it and you will get 4e^-x - 1
Yes, what dumbcow said. Then you can take the integral of each part.
FTC simply says it CAN be done; then you apply the techniques :)
I don't know how to apply the techniques haha, that's why I'm here!
the equation editor seems to have distorted the equation ; can you verify it?
I was given a take-home test, and I'm supposed to teach myself definite integrals and have it due tomorrow.
FTC says the definite integral = F(1) - F(-1) but you have to find F(x) by taking anti-derivative of f(x)
\[\int\limits_{-1}^{1} 1/(e^x) (4-e^x) dx\]
If you integrate 4e^-x, you would get -4e^-x. Then, integrate 1 and you get x So then you have -4e^-x - x evaluated from -1 to 1
\[\int\limits_{-1}^{1} \frac{1}{e^x} (4-e^x) dx\]
^^ that
frac{top}{bottom} in the editor makes for fancy fractions :)
Ooo, ok!
integrate {4/(e^x) - 1} dx
4 (ln(e^x)) - x
do what math93 said
4x-x = 3x F(x) = 3x right?
no F(x) =-4e^-x - x
close lol
\[ \frac{-4}{e ^{x}}-x\] evaluated from -1 to 1
coulda thunked that 1/u integrates to ln(u)....
4e^-x is just as good i spose :)
if you sub in your values, you get (-4e^-1 - 1)-(-4e^-1+1)
i see it..... just blind in my old age
After the values are substituted in, do I just simplify?
yes
So is the final answer (-2)?
Yeah, that's what I got
So is the answer just (-2) by itself? Or is there anything on the opposite side of the equal sign?
the integral of the original problem = -2, so "-2" is the final answer
Alright, I appreciate the help, I'll use this one as an example to hopefully finish the rest of the problems I have, cheers!
Good luck!
Thank you!!

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