anonymous
  • anonymous
Find the definite integral using the Fundamental Theorem of Calculus.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\int\limits_{-1}^{1} e^-x (4-e^x) dx\]
anonymous
  • anonymous
see the thing is iruno how to break this ice
anonymous
  • anonymous
is exactly what i need help with

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.