Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

artofspeed

  • 3 years ago

integral: are these two expressions equal?

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

    \[\int\limits_{0}^{a}f(a-x)dx = \int\limits_{}^{}f(0)dx-\int\limits_{}^{}f(a)dx = \int\limits_{a}^{0}f(x)dx\]

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

    You can check this on example. Try \(f(x)=x^2, a=1.\)

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

    It will more easy if you take \(f(x)=1\).

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

    so it this whole expression correct?

  5. sirm3d
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    only the first and last expressions can be equated.

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

    actually, the first and last aren't equal. But what's wrong in the expression?

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

    \[\int\limits_{0}^{a}f(a-x)dx \ne \int\limits_{}^{}f(0)dx-\int\limits_{}^{}f(a)dx = \int\limits_{a}^{0}f(x)dx\]The primitive of \(f(a-x)\) is \(-\int f(a-x)dx\) and not \(\int f(a-x)dx\). You can check this by taking derivative. Now, I think you can answer your question by yourself.

  8. 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