Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jackkim4

  • 2 years ago

Find the interval [a,b] for which the value of the integral b s(2+x-x^2)dx a is maximum

  • This Question is Closed
  1. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    help me :'(

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

    is this your question ?\[\int\limits_a^b(2+x-x^2)\text dx\]

  3. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes!!! sry first time here....

  4. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is the answer [-1, 2] or [-1,1/2] ??

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

    as @UnkleRhaukus pointed out, you have maximize \[ \large F(a,b)=\int_a^b(2+x-x^2)\,dx \]

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

    which one gives u the greatest area?

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

    *value, sorry.

  8. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    doesnt [-1, 1/2] wait no... it's [-1, 2]

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

    what did you get when you integrated

  10. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    27/6 ???

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

    which interval?

  12. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    [-1,2]

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

    \[\int\limits_a^b(2x^0+x^1-x^2)\text dx=\frac{2x^1}1+\frac{x^2}2-\frac{x^3}{3}\Big|_a^b\]\[=2(b-a)+\frac{(b-a)^2}2-\frac{(b-a)^3}{3}\] right?

  14. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes!

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

    actually i think i made a mistake

  16. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it's separated right

  17. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    [2b+b^2/2-b^3/3]-[2a+2a^2/2-a^3/3]

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

    \[\int\limits_a^b(2x^0+x^1-x^2)\text dx=\frac{2x^1}1+\frac{x^2}2-\frac{x^3}{3}\Big|_a^b\]\[\qquad\qquad=\left({2b}+\frac{b^2}2-\frac{b^3}3\right)-\left({2a}+\frac{a^2}2-\frac{a^3}3\right)\]yeahs

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

    so when is this maximum

  20. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    at a= -1 b= 2 ! right?

  21. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Maximize F(b) by derivative, minimize F(a) by derivative.

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

    \[=b\left({2}+\frac{b}2-\frac{b^2}3\right)+a\left(-{2}-\frac{a}2+\frac{a^2}3\right)\]

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

    \[=6b\left(12+3b-2b^2\right)+6a\left(2a^2-3a-12\right)\]

  24. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\large F \prime (b)=2+b-b^2=0\]\[\large \text{max at } b=2\]\[\large F \prime (a)=2+a-a^2=0\]\[\large \text{max at } a=-1\] interval: [-1, 2]

  25. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wow, my answer is among the choices given.

  26. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    omg lol

  27. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    typo mistake. it should be min at a = -1

  28. jackkim4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yayyyyyy tytytyty! :')

  29. 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.