A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Differentiate: 1/(2x-1)^(1/2) dx from x=5 to x=13

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

    Use a u sub, and then F(13)-F(5)

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

    if you can differentiate \[\int\limits 1/x dx\] then you will know how to do it. do you need more help ?

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

    Yes I do, sorry.

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

    your integral looks awfully like 1/x, it's just shifted a little. you you can guess that it is the family of 1/x. can you integrate 1/x ?

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

    log x +c?

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

    it's actually lnx + C

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

    That's what I meant, lol

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

    okay just making sure

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

    I just really don't understand definite integrals.

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

    now your goal is to make the integral look like that by letting u = 2x+1

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

    oops, never mind about lnx, i did not see the ^1/2 part. so it will be a family of \[\int\limits 1/\sqrt(x)\]

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

    But then what?

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

    after letting u = 2x-1, \[\int\limits 1/\sqrt(u) dx\]

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

    is what you are going to get, but the problem is that the integrand is now a function of u, which cannot be integrated over x. so you have to over come that by figuring out what "dx" is. that technique is the so-called u-substitution. do you know how to find dx ?

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

    No

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

    okay, so u = 2x-1 right ? if you differentiate both sides with respect to x, d/dx(u) = d/dx(2x-1) d/dx(u) = 2 do you get this so far ?

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

    Yes

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

    so if you multiply dx on both sides and divide 2 on both sides, you will get 1/2 du = dx this is what is happening, but it is traditional and easier to say u=2x-1 du = 2 dx by differentiating both sides

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

    Gotcha

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

    so once you substitute dx with the above equation, your integral becomes\[1/2\int\limits 1/\sqrt(u) du\]

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

    now it is important to know that the limits of the integration will change as well, unless you want to know how to do that I won't go into the detail. to avoid having to change the limits, you will find out the indefinite integral first, then substitute 2x-1 back into u. that way you can plug in the limits again.

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

    so the answer is 2?

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

    \[1/2\int\limits 1/\sqrt(u) du = 1/2 *1/2*(u^{1/2})+C\]

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

    1/4(2x-1) + C =F(x) so F(13) -F(5) is your answer. just as a reminder, C will not matter so you can ignore it

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

    woops\[1/4 \sqrt(2x-1) +C\] is what I meant

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

    it seems like the answer will be 3/4

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

    Oh, ok, I see. Thanks!!! Can you help me with a couple word problems too?

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

    I need to go soon, so I can help you with one of them. ask me the one that you think need most help

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

    A manufacturer has been selling flashlights at $6 a piece, and at this price consumers have been buying 3000 flashlights per month. The manufacturer wishes to raise the price and estimates that for each $1 increase in price, 1000 fewer flashlights will be sold each month. The manufacturer can produce the flashlight a cost of $4 per flashlight. At what price should the manufacturer sell the flashlights to generate the greatest profit?

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

    okay so what do you not get from this problem ?

  31. 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.