anonymous 5 years ago Find the definite integral using the Fundamental Theorem of Calculus.

1. anonymous

$\int\limits_{-1}^{1} e^-x (4-e^x) dx$

2. anonymous

see the thing is iruno how to break this ice

3. anonymous

is exactly what i need help with

4. anonymous

That's e^(-x) by the way And I know, I'm so lost.

5. anonymous

haha yeh this crap makes people lost in formulas man

6. anonymous

so define the fundamental thrm of calculus; then see how that applies :)

7. anonymous

My real question is, I don't know where to start with this problem.

8. anonymous

start by defining the FTC and see how it applies lol.... that is the start

9. anonymous

That does nothing for me.

10. anonymous

expand it and you will get 4e^-x - 1

11. anonymous

Yes, what dumbcow said. Then you can take the integral of each part.

12. anonymous

FTC simply says it CAN be done; then you apply the techniques :)

13. anonymous

I don't know how to apply the techniques haha, that's why I'm here!

14. anonymous

the equation editor seems to have distorted the equation ; can you verify it?

15. anonymous

I was given a take-home test, and I'm supposed to teach myself definite integrals and have it due tomorrow.

16. anonymous

FTC says the definite integral = F(1) - F(-1) but you have to find F(x) by taking anti-derivative of f(x)

17. anonymous

$\int\limits_{-1}^{1} 1/(e^x) (4-e^x) dx$

18. 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

19. anonymous

$\int\limits_{-1}^{1} \frac{1}{e^x} (4-e^x) dx$

20. anonymous

^^ that

21. anonymous

frac{top}{bottom} in the editor makes for fancy fractions :)

22. anonymous

Ooo, ok!

23. anonymous

integrate {4/(e^x) - 1} dx

24. anonymous

4 (ln(e^x)) - x

25. anonymous

do what math93 said

26. anonymous

4x-x = 3x F(x) = 3x right?

27. anonymous

no F(x) =-4e^-x - x

28. anonymous

close lol

29. anonymous

$\frac{-4}{e ^{x}}-x$ evaluated from -1 to 1

30. anonymous

coulda thunked that 1/u integrates to ln(u)....

31. anonymous

4e^-x is just as good i spose :)

32. anonymous

if you sub in your values, you get (-4e^-1 - 1)-(-4e^-1+1)

33. anonymous

i see it..... just blind in my old age

34. anonymous

After the values are substituted in, do I just simplify?

35. anonymous

yes

36. anonymous

So is the final answer (-2)?

37. anonymous

Yeah, that's what I got

38. anonymous

So is the answer just (-2) by itself? Or is there anything on the opposite side of the equal sign?

39. anonymous

the integral of the original problem = -2, so "-2" is the final answer

40. 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!

41. anonymous

Good luck!

42. anonymous

Thank you!!