A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

How would I do this?

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

  2. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    sub \(u=2x\)

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

    Hmm... but I don't have the function... Im kind of confused

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    \[\int\limits_0^2 f(2x)\,dx~~\stackrel{u=2x}{=}~~ \frac{1}{2}\int\limits_0^4 f(u)\,du = \frac{1}{2}*20=10\]

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

    Why does the limit of integration change from 4 to 2?

  6. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    scratch that, lets work it again from beginning

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    you want to evaluate \[\int\limits_0^2f(2x)\, dx\] substitute \(u=2x \implies du=2dx\implies dx=\dfrac{du}{2}\)

  8. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    next work the bounds, as \(x\to 0\), what does \(u\to\) ? as \(x\to 2\), what does \(u\to\) ?

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

    1) x -> 0, u -> 0 2) x -> 2, u -> 4

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    so upon substitution, bounds change from (0, 2) to (0, 4) and the differential changes from dx to du/2 plug them in

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

    okay, so then that's \[\int\limits_{0}^{4}f(u) \frac{ du }{ 2 }\] and then the 1/2 comes out of the integral

  12. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    Yes, next recall that the variable in definite integral is "dummy" \[\int\limits_a^b f(\color{red}{x})\,d\color{red}{x} = \int\limits_a^b f(\color{red}{t})\,d\color{red}{t}=\int\limits_a^b f(\color{red}{\spadesuit})\,d\color{red}{\spadesuit}\]

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

    right

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ohhh now I get what's happening!

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

    @ganeshie8 Thanks so much!

  16. 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.