A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. y=7x^2 y^2 = (1/7)x find area of the region

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

    this sounds familiar ;)

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

    helloo and yes D: i feel like i did all the steps right, but its not the right answer >< i set both the equations to eachother to find the boundaries, thats the first step right?

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

    7x^2 = sqrt of (1/7)x i square both sides to get rid of the radical so im left with 7x^4 = (1/7)x i multiply both sides by 7, i get 49x^4 = x subtract x from both sides, you get 49x^4 - x = 0

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

    can we double int it?

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

    i believe so

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

    y = sqrt(1/7x) y=7x^2 {SS} dy dx ; x=[0,1]; y = [7x^2,sqrt(1/7x)] right?

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

    {S} sqrt(1/7x) - 7x^2 dx ; [0,1]

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

    how did you get 0 and 1 ?

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

    sqrt(1/7) 2x sqrt(x/3) - 7/x^3/3

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

    thats where your graphs intersect at

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

    to find the intersection, you set the equations equal to eachother right?

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

    2sqrt(1/21)-7/3 i believe is the area

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

    yes

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

    did i miss that up lol

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

    thats what i did at first, but i got x = 0 and x = cube root of 1/49

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

    y= 7x^2; and x=7y^2

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

    i could be wrong, trying tis in my head lol

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

    lol youre right, but wouldnt we have to set that second equation that y is on one side by itself, not x ?

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

    y=sqrt(1/7x) ; y = 7x^2 1/7x = 49x^4 49 x^4 - 1/7x = 0 x(49x^3 - 1/7) = 0 x=0 to.....my brain shut off lol

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

    1/7x(343x^3 - 1) = 0

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

    x = 0 and x = cube root of 1/343 ?

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

    wolfram tells me that (1,1/7) is the solution to these; lets try that out :)

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

    sqrt(1/7*1) = sqrt(1/7) 7*1 = 7....... ack!!

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

    lol xD

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

    hmm

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

    deep breath....... ok

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

    y=7x^2 and y^2 = 1/7x right?

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

    yup

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

    we know zero is a good one

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

    yes

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

    y =1 1 7 ---- = 1/7; at x=1/7, y = 1/7 ; thats y=x^2 7 7

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

    at x = 1/7; we get y = sqrt(1/7 1/7) = sqrt(1/49) = 1/7

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

    so lets int this thing from 0 to 1/7 :)

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

    im sorry im a little lost, how did you get 1/7 for x ?

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

    [S] 7x^2 - sqrt(1/7x) dx ; [0,1/7] ....i guessed and was right :)

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

    xD awesome haha

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

    i had an inclination, but couldnt verify it till i just plugged it in ;)

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

    i know that this is 2 parabolas at right angles to each other; so they only meet at 2 point, to that one works and has to be it lol

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

    7x^3/3 - 2sqrt((7x)^3)/3 ??

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

    is the 2aqrt((7x)^3)/3 the same as 2x^(3/2) divided by 21 ? cuz i put sqrt of 1/7 as (1/7)^(1/2) and found the antiderivative like that

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

    sqrt(1/7)* sqrt(x) = sqrt(1/7)* 2sqrt(x^3)/3 7x^3/3 - 2sqrt(1/7x^3)/3 right?

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

    the sqrt(1/7) is actually a constant, so we can pull it out of the way and just do sqrt(x)

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

    sqrt(ab) = sqrt(a) * sqrt(b)

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

    ohhh i see

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

    1/49(3) - 2sqrt(1/7^4)/3 should be the area

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

    how comes its (1/7^4) ?

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

    1 2sqrt(1/2401) --- - ------------ 147 3 (1/7) * (1/7)^3 = 1/7^4

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

    as long as i integrated it right, and im pretty sure i did :)

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

    dbl check it tho ;)

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

    im going over it right now :D

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

    \[\int\limits_{} (7x^2 - \sqrt{\frac{1}{7}x} )dx\]

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

    http://www.wolframalpha.com/input/?i=int%287x^2+-sqrt%28x%2F7%29%29dx++from+0+to+1%2F7

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

    id take the absolute value of that :)

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

    thats what i got too :) and i jus ttake the absolute value of that since its negative right ?

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

    correct; just means we got the wrong order

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

    see... http://www.wolframalpha.com/input/?i=int%28sqrt%28x%2F7%29-7x^2%29dx++from+0+to+1%2F7

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

    gotcha. thank you once again. always coming to my rescue :D haha youre the best !

  58. 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.