A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

Evaluate the intragural. 3y(7+2y^2)^1/2 dy

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

    Does anyone have any idea?

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

    \[u=7+2y^2\]\[du=4ydy\]\[\int3y(7+2y^2)^{1/2}dy=\frac34\int u^{1/2}du\]

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

    Wait. So how did that 3y in front of the u just dissapear?

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

    I just pulled it outside the integral sign

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

    \[\int cf(x)dx=c\int f(x)dx\]

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

    Even though its 3y(u)^1/2? I thought if it was 3+ you could

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

    Im just not getting where the y went

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

    \[u=7+2y^2\]\[du=4ydy\to ydy=\frac14du\]\[\int3y(7+2y^2)^{1/2}dy=3\int (7+2y^2)^{1/2}ydy\]I just pulled the three out and put ydy together, so now I can sub in my expressions for 7+2y^2 and ydy that I got above:\[3\int (7+2y^2)^{1/2}ydy=\frac34\int u^{1/2}du\]let me know if something is still eluding you.

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

    a little slower on the last step:\[3\int (7+2y^2)^{1/2}ydy=3\int(u)^{1/2}(\frac14du)=\frac34\int u^{1/2}du\]

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

    I sorta get it I think. Just not sure how ydy becames (1/4du) when du did equal 4ydy. Shouldnt it be (1/4du)y?

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

    the u sub works such that we need to wind up with \[\int u^ndu\]watch the terms that we get from our substitution\[u=7+2y^2\]\[du=4ydy\]\[ydy=\frac14du\]so we rearrange our integral so that we replace ydy by 1/4du if we had ydu we couldn't integrate, so that would not help

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

    \[3\int (7+2y^2)^{1/2}(ydy)=3\int(u)^{1/2}(\frac14du)=\frac34\int u^{1/2}du\]see how ydy got replaced?

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

    Oh I think I get it. Thanks a lot

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

    u-subs can be tricky at first, but with practice it's a flash :D

  15. 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.