Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

BaoZhu

  • 9 months ago

integral x^3(sqrt(16-x^2)dx can someone check if my answer is right, (-1024/3)((sqrt(16-x^2)/(3)))^3+(1024/5)((sqrt(16-x^2)/(3)))^5+C

  • This Question is Closed
  1. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    May I ask what method of integration you chose?

  2. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    first i used trig. sub. a-x^2, gives x=4sintheta, and then i used trig. integral of u-sub.

  3. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you could have done this with just an algebraic substitution

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

    \[u=16-x^2 => du=-2x dx \] \[x^2=16-u \] So \[\int\limits_{}^{}x^2 \sqrt{16-x^2} dx=\frac{-1}{2}\int\limits_{}^{}x^2 \sqrt{16-x^2} (-2x) dx\] \[=\frac{-1}{2}\int\limits_{}^{}(16-u) \sqrt{u} du \] \[=\frac{-1}{2}\int\limits_{}^{}(16 u^\frac{1}{2}-u^\frac{3}{2}) du\]

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

    but it's x^3, not x^2

  6. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    integral x^3*sqrt(16-x^2)dx

  7. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I missed an x in that first part but and that next equation you see i have x^2 times x which is x^3

  8. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    expression* that follows that first equal sign

  9. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you see?

  10. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    one more question

    1 Attachment
  11. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you find P(x) as a 2nd degree taylor polynomial yet?

  12. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i do not know where to start......

  13. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[P(x) \approx P(r)+P'(r)(x-r)+\frac{1}{2}P''(r)(x-r)^2 \] This is what they want you to use.

  14. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    They want you to use r as 5 and plug in the values they gave you for P'(5) and P''(5) Then they want you to find P(5.5) approximately using the resulting equation

  15. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so for 5, i got p5(x)=120000-40000(x-5)+22500(x-5)^2, is this right so far?

  16. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[P(x)=45000+\frac{45000}{120000}(x-5)+\frac{1}{2} \frac{45000}{-40000}(x-5)^2 \]

  17. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We are given \[P(5)=45000; \text{ and } 120000 \cdot P'(5)=45000 ; \text{ and } -40000 \cdot P''(5)=45000\]

  18. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That is how I got what was P'(5) and P''(5) and P(5)

  19. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We will use that P I wrote to approximate the value of portfolio bonds when r is 5.5.

  20. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh are those commas?

  21. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol

  22. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I can't read.

  23. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok what you wrote is good then

  24. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So use your equation not mine to approximate P(5.5)

  25. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but how will it turn the equation into just 1 number?solve for x?

  26. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i don't understand

  27. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[P(x) \approx 120000-40000(x-5)+45000(x-5)^2 \] You can find P(5.5) It will result in one number

  28. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    there is only one variable

  29. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and you are asked to replace that variable x with 5.5

  30. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this will give you P(5.5)

  31. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It is just like if i asked you to evaluate f(2) given f(x)=x-5 you would say f(2)=2-5=-3

  32. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh thank you so much, i thought i have to replace 5.5 in as in term of r

  33. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and don't forget the 1/2 part on that one part

  34. BaoZhu
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but now i got it, 105625 would be the answer

  35. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah but you aren't given P''(5.5) or P'(5.5) or P(5.5) so that would be impossible

  36. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no that isn't the answer

  37. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    don't forget the half part on that last term

  38. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[P(x) \approx 120000-40000(x-5)+\frac{1}{2} 45000(x-5)^2 \]

  39. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    which you wrote earlier has 22500 which is fine

  40. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm talking about for that 1/2*45000 part you simplified it earlier to 22500

  41. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.