A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

e^.07(10-t)[10,1) find the definite integral

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    [10,1) is a little backwards... (1,10] is that e^.07 times (10-t)? or is the last part included in the exponent?

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

    \[\int\limits_{1}^{10} e^.07(10-t)\]

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so it aint included as the exponent..makes it alittle easier :)

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    e^.07 is a constant, so pull it out of the way

  5. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (S) (10-t) dt -> 10t - (1/2)t^2 F(t) = [10t - (t^2)/2] e^.07

  6. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    F(10) - F(1) will be the answer

  7. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (100 - 50)e^.07 - (10-.5)e^.07 (50 - 9.5) e^.07 (40.5) e^.07 if I did it right in me head :)

  8. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that might be alittle off, did you mean to exclude 1 as an option?

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

    no 1 is included. now I'm understanding

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    whew!!.... cause in the top {10,1) means everything from 10 to 1 but not including 1 :)

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

    no i just want it for 10 and 1

  12. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then were good with it :) I got some idea for how to find it if it approaches 1, but nothing ti be sure about :)

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

    Ive got another one its its kinda hard what you think

  14. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I can take a stab at it..... im ok with failure :)

  15. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it one thats already posted? or you need to write it up?

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

    im going to write it now

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

    \[\int\limits_{0}^{15}\]e^0.05e^.06(15-t)

  18. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    to clean it up... is that: e (e) (15-t) ??

  19. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or is that: e^e^(15-t)?

  20. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i assume the first one :)

  21. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    recall that like bases when multiplies add exponents, for example: 5^3 5^5 = 5^(3+5) = 5^8 so, e^.06 e^.06 = e^.11 which is still a constant and can be pulled out...

  22. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can see the typo right....

  23. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that leaves us with: (S) 15-t dt -> 15t - (t^2)/2 | [15,0] F(t) = [15t - (t^2)/2] e^.11 since F(0) = 0 the only important on is F(15) F(15) = [15(15) - 15(15)/2] e^.11 = [225 - 112.5] e^.11 F(15)= 112.5 e^.11

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

    \[\int\limits_{0}^{15}e^.05e.06(15-t)\]

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

    this is how it looks exactly will u get the same answer or does this makes a difference

  26. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is that .06 an exponent?

  27. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (e^.05) (e^.06) (15-t) is what I integrated :)

  28. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that equation option down there is useful for some things, but I can never get it to do what I want....

  29. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{0}^{15} e^{.05} e^{.06} \left( 15-t \right)\]

  30. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[= (112.5) e ^{.11}\]

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

    it its e^0.5.e^.06 the 15-t is beside the .06 in exponential form

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

    ok so what will happen to the ^(15-t)

  33. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{0}^{15} e ^{.05} e^{.06\left( 15-t \right)}\]

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

    yes that's exactly what it is

  35. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok....we can pull out that first e, its nothing but a constant

  36. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    go ahead and distribute the .06 thru the (...)

  37. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    e^(.8 - .06t) right?

  38. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (.9 - .06t)

  39. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If we can get this into the form: (S) Du e^u , then it suits up to e^u....does that make sense?

  40. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    think back to derivatives... e^2x goes down to 2 e^2x right? does that ring a bell?

  41. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so... (S) 2 e^2x would equal just e^2x does that help out?

  42. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    our exponent here (.8-.06t) derives to: -.06 right? so we need to modify this set up to include an (-.06) without actually changing the value of the set up... what number can we multiply ANY number by to get the same value back? x times ? equals x ??

  43. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    d (e^x) dx --- = ---- e^x dx dx Or to right it another way: Dx(e^x) -> Dx e^x Dx(e^7x) -> Dx(7x) e^7x -> 7 e^7x right>

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

    not sure im getting the last part

  45. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok.... tell me what your having difficulites with and I can help iron out the wrinkles :)

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

    ok the (.8-.06t) not getting the dirivitive of this

  47. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im thinking it involves the chain rule...which I think should be called the "gear"rule...

  48. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I want you to think of a box of gears that are all meshed together so that when you turn the very first one, it has an effect on all the rest of them. each gear in turn is turning another correct?

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

    yes i understand how you get the -.06 is this where we use the [15,0]

  50. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not yet, we havent gotten to our initial function yet, we still need to find a way to get there first.

  51. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we have a function: e^u that depends on "u" for its value right? u = .8 -.06t and so the value of "u" depends on the value of "t" right?

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

    why did we substititute?

  53. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we substitued values to see how the original function behaves. What we need in order to integrate this original function is to modify the way it looks without changing its "value". we can easily integrate the function Du e^u to get e^u so this is our goal. We need to modify the "shape" of our original function so that it matches the "easy to integrate" function without changing the "value" of our original function.

  54. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what number do we know of that is used to obtain the same "value" but a different "shape" of a function? x times ? = x ??

  55. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    for example: say you only have a 20 dollar bill, and you want to buy some bubble gum for 1.00 but the cashier has no change to plit your $20. How can you purchase the bubble gum? by changing your $20 into a bunch of $1 bills... that is all we are wanting to do here.... so that we can make life easier for us

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

    ok

  57. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We have e^u we WANT Du e^u what value does Du have to be?

  58. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Du is probably a bad name for that.... let me ask this.. what do we have to multiply (e^u) by in order to keep the same "value" e^u times ____ = e^u ?

  59. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    think 1....think 1.... 1 times e^u = e^u right?

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

    right

  61. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    does Du/Du = 1?

  62. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    does (-.06)/(-.06) = 1 ??

  63. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -.06 e^.05 (S) ----- e^(.8 -.06t) dt -.06 look close to what we want it to be?

  64. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if your unsure, tell me what your doubts are.... cause I can be rather stupid at times and mess alot of simple things up :)

  65. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in essense, we want to slide that bottom (-.06) out of the way since it is a constant we can do that and put it under the left side. that leaves the integrand to be -(e^.05)/.06 [S] -.06 e^(.8-.06t) dt -> e^(.8-.06t) F(t) = - [(e^.05)/.06] [e^(.8-.06t)]

  66. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or put another way: - e^(.85 - .06t) F(t) = ------------- .06

  67. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (Constants) [S] Du e^u du becomes (Constants) (e^u) is all we did in a nutshell

  68. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I gotta head to class for the next few hours... if your still lost, go ahead and post it for everyone to see :) Ciao

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.