A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Let R be the region bounded by the curve y = ln (x), the x-axis and the line x = e. Find the area of R. I need a quick answer with minimal work shown. Thanks

  • This Question is Closed
  1. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 8

    |dw:1435595958782:dw|

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

    Is there a graph you are suppose to give us?

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

    That's all the question says.

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

    ok, so you have to integrate that from x=1 to x=e

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

    1 Attachment
  6. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 8

    what I drew, is the picture, and x=1 is the limit of integration, because that is where the area above the x-axis starts, and x=e is the limit of integration because your region is bounded by x=e.

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

    the regeion is from x=1 to x=e

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

    so do integral of lnx from 1 to e

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

    \(\Large\color{slate}{\displaystyle\int\limits_{1}^{e}{\rm Ln}(x)~dx}\) like this.

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

    So just set it up and solve it

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

    yup

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

    ?

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

    you know the integral of ln(x) right?

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

    Yes xlnx - x

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

    yup, that is right. Now you have to plug in the limits of integration.

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

    \(\Large\color{slate}{\displaystyle\int\limits_{1}^{e}{\rm Ln}(x)~dx=\left(x{\rm Ln} {\tiny~}x~-~x\right)~{\Huge|}_{1}^{e}}\)

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

    Yeah I got that now thanks. How would I find the volume of the same problem on the x axis and also on the y axis?

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

    Volume? Do you mean that the region we drew is rotated around some line?

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

    Yeah I got that now thanks. How would I find the volume of the same problem on the x axis and also on the y axis?

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

    Yep exactly that

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

    you mean the area, not the volume? if volume, then it is 3d, and probably this R is rotated around some line y=C or x=C. if area, then what area do you exactly what to find?

  22. 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.