A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

How do you anti-derive x(2-x)^2?

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

    you have to take the integral

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

    Would you mind showing me step by step?

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

    I'm a little rough at this but I can try to help. I would go ahead and multiply through before calculating the integral. So you would have \[x(2-x)(2-x)\] then you would foil and multiply through by x. You end up with an integral that looks like this \[\int\limits 4x-4x ^{2}+x^3 dx\]

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

    Check my work... Like I said I'm a little rough at this. I believe you use a basic integration formula for each of those numbers...

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

    correcto mundo

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

    \[\int\limits 4x dx = 4(1/2)x ^{2}\]

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

    You can make it much simpler by letting u=2-x and du=-1*dx. Then, you get -∫u^2*(2-u) du which expands to -∫2u^2-u^3 du = -[2u^3/3 - u^4/4] + c = -2(2-x)^2/3 + (2-x)^4/4 + c, if I'm not mistaken. MtHaleyGirl's solution is correct, but just seems like a lot more tedious multiplication than is necessary.

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

    I DO take the long way... Scared of substitution but I just need a little practice. Good tip. Maybe it will make MY life easier.

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

    Yesss, substitution makes life so much easier later on, once you get confident with it. It's an absolute must for a lot, if not all, of advanced techniques of integration.

  10. 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.