Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

kjp92123

  • 3 years ago

Find the definite integral using the Fundamental Theorem of Calculus.

  • This Question is Closed
  1. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  2. 92saadz
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    see the thing is iruno how to break this ice

  3. 92saadz
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is exactly what i need help with

  4. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. 92saadz
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    haha yeh this crap makes people lost in formulas man

  6. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  7. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  8. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  9. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That does nothing for me.

  10. dumbcow
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  11. math93
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  12. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  13. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  14. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  15. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  16. dumbcow
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  18. math93
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  20. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ^^ that

  21. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  22. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ooo, ok!

  23. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  24. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4 (ln(e^x)) - x

  25. dumbcow
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do what math93 said

  26. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  27. dumbcow
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  28. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    close lol

  29. math93
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  30. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  31. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  32. math93
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  33. Im_Hotep55
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  34. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  35. math93
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  36. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So is the final answer (-2)?

  37. math93
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, that's what I got

  38. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  39. math93
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  40. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good luck!

  42. kjp92123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you!!

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.