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

1. kjp92123 Group Title

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

see the thing is iruno how to break this ice

is exactly what i need help with

4. kjp92123 Group Title

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 Group Title

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

7. kjp92123 Group Title

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

8. Im_Hotep55 Group Title

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

9. kjp92123 Group Title

That does nothing for me.

10. dumbcow Group Title

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

11. math93 Group Title

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

12. Im_Hotep55 Group Title

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

13. kjp92123 Group Title

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

14. Im_Hotep55 Group Title

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

15. kjp92123 Group Title

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

16. dumbcow Group Title

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 Group Title

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

18. math93 Group Title

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 Group Title

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

20. kjp92123 Group Title

^^ that

21. Im_Hotep55 Group Title

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

22. kjp92123 Group Title

Ooo, ok!

23. Im_Hotep55 Group Title

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

24. Im_Hotep55 Group Title

4 (ln(e^x)) - x

25. dumbcow Group Title

do what math93 said

26. Im_Hotep55 Group Title

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

27. dumbcow Group Title

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

28. Im_Hotep55 Group Title

close lol

29. math93 Group Title

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

30. Im_Hotep55 Group Title

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

31. Im_Hotep55 Group Title

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

32. math93 Group Title

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

33. Im_Hotep55 Group Title

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

34. kjp92123 Group Title

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

35. math93 Group Title

yes

36. kjp92123 Group Title

So is the final answer (-2)?

37. math93 Group Title

Yeah, that's what I got

38. kjp92123 Group Title

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

39. math93 Group Title

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

40. kjp92123 Group Title

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 Group Title

Good luck!

42. kjp92123 Group Title

Thank you!!