Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

math456

  • 3 years ago

How do I do this?

  • This Question is Closed
  1. math456
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int\limits_{0}^{9}f(x)dx=37; \int\limits_{0}^{9}g(x)dx=16\]

  2. math456
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Find: \[\int\limits_{0}^{9}[2f(x)+3g(x)]dx\]

  3. phi
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the integral is "linear" in other words, for a constant "a" \[ \int\limits_{0}^{9} a f(x)dx = a\int\limits_{0}^{9} f(x)dx \]

  4. math456
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so in this case \[2\int\limits_{0}^{9} x.dx\]??

  5. phi
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and you can separate integrals (assuming they have the same limits \[ \int\limits_{0}^{9} f(x) + g(x) dx= \int\limits_{0}^{9} f(x)dx + \int\limits_{0}^{9} g(x)dx\]

  6. phi
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    not x , f(x) so separate the problem into \[ 2\int\limits_{0}^{9} f(x)dx + 3\int\limits_{0}^{9} g(x)dx \]

  7. math456
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yea right! so \[37x(9,0)+16x(9,0)\]

  8. phi
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't know about the x(9,0) part just replace the integral with the number they say it is equal to \[ 2\cancel{(\int\limits_{0}^{9} f(x)dx)}37 + 3\int\limits_{0}^{9} g(x)dx \] and do the same for the other, it is 16

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

    I am trying to show you sub in 37 for the result of the first integral

  10. math456
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh alright, i got it!

  11. math456
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so its 2(37) + 3(16) = 122

  12. math456
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks @phi :)

  13. 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