Results 1 to 4 of 4

Math Help - Definite Integrals - Please Help!

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    36

    Definite Integrals - Please Help!

    I cannot figure out this question. I really need help from beginning all the way to end.

    Let ∫9(bottom) 12 (top) f(x) dx = 9,
    ∫9 (bottom)10(top) f(x) dx=8,
    ∫11 (bottom)12(top) f(x)dx = 1.


    Find ∫10 (bottom) 11 (top) f(x)dx=

    and ∫11 (bottom) 10 (top) (9 f(x)− 8)dx=
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member apcalculus's Avatar
    Joined
    Apr 2009
    From
    Boston
    Posts
    293
    Quote Originally Posted by derekjonathon View Post
    I cannot figure out this question. I really need help from beginning all the way to end.

    Let ∫9(bottom) 12 (top) f(x) dx = 9,
    ∫9 (bottom)10(top) f(x) dx=8,
    ∫11 (bottom)12(top) f(x)dx = 1.


    Find ∫10 (bottom) 11 (top) f(x)dx=

    and ∫11 (bottom) 10 (top) (9 f(x)− 8)dx=

    If this function is continuous, then the integral from 9 to 12 can be described as the sum of the following integrals:

    9 to 10 equals 8
    10 to 11 is unknown
    11 to 12 equal 1


    8 + 1 + unknown = 9

    So the integral from 10 to 11 is zero.

    For the second part, use the properties of integrals to write it as

    9 INTEGRAL(f(x)) - INTEGRAL(8) with bounds as given.

    Good luck!!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    36
    I cant figure out how to calculate the second part...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by derekjonathon View Post
    I cant figure out how to calculate the second part...
    You will need to show a bit more effort. Reviewing the relevant theory in your notes and/or textbook will help.

    You have \int_{11}^{10} (9 f(x) - 8) \, dx. And you've been told to use the basic properties of integrals. Doing so gives:

    -9 \int^{11}_{10} f(x) \, dx + 8 \int^{11}_{10} \, dx. Your jobs are:

    1. Calculate this.

    2. Fill in the steps that led to it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: December 5th 2011, 05:21 PM
  2. Replies: 4
    Last Post: April 13th 2011, 02:08 AM
  3. Definite integrals.
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 3rd 2011, 08:57 PM
  4. Definite Integrals
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 24th 2009, 03:44 AM
  5. Definite integrals
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 3rd 2009, 11:53 PM

Search Tags


/mathhelpforum @mathhelpforum