## kjp92123 3 years ago Find the definite integral using the Fundamental Theorem of Calculus.

1. kjp92123

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

see the thing is iruno how to break this ice

is exactly what i need help with

4. kjp92123

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

haha yeh this crap makes people lost in formulas man

6. Im_Hotep55

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

7. kjp92123

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

8. Im_Hotep55

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

9. kjp92123

That does nothing for me.

10. dumbcow

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

11. math93

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

12. Im_Hotep55

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

13. kjp92123

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

14. Im_Hotep55

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

15. kjp92123

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

16. dumbcow

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

17. kjp92123

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

18. math93

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. Im_Hotep55

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

20. kjp92123

^^ that

21. Im_Hotep55

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

22. kjp92123

Ooo, ok!

23. Im_Hotep55

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

24. Im_Hotep55

4 (ln(e^x)) - x

25. dumbcow

do what math93 said

26. Im_Hotep55

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

27. dumbcow

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

28. Im_Hotep55

close lol

29. math93

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

30. Im_Hotep55

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

31. Im_Hotep55

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

32. math93

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

33. Im_Hotep55

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

34. kjp92123

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

35. math93

yes

36. kjp92123

So is the final answer (-2)?

37. math93

Yeah, that's what I got

38. kjp92123

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

39. math93

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

40. kjp92123

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. math93

Good luck!

42. kjp92123

Thank you!!