Results 1 to 3 of 3

Math Help - Fundamental Theorem of Calculus

  1. #1
    Newbie
    Joined
    Jan 2007
    Posts
    19

    Fundamental Theorem of Calculus

    How do you use Part 1 of the fundamental theorem of calculus to find the derivative of:

    g(x)=integral of (9*cos(t))/(t) from 3 to x^(1/2)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2006
    Posts
    679
    Awards
    1

    Re:

    Quote Originally Posted by asnxbbyx113 View Post
    How do you use Part 1 of the fundamental theorem of calculus to find the derivative of:

    g(x)=integral of (9*cos(t))/(t) from 3 to x^(1/2)?
    RE:
    Attached Thumbnails Attached Thumbnails Fundamental Theorem of Calculus-37.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by asnxbbyx113 View Post
    How do you use Part 1 of the fundamental theorem of calculus to find the derivative of:

    g(x)=integral of (9*cos(t))/(t) from 3 to x^(1/2)?
    this page may help a bit

    you may also want to look up "the second fundamental theorem of calculus" on wikipedia or some other source

    g(x) = \int_{3}^{\sqrt {x}} \frac {9 \cos t}{t} dt

    \Rightarrow g'(x) = \frac {d}{dt} \int_{3}^{\sqrt {x}} \frac {9 \cos t}{t}dt

    \Rightarrow g'(x) = \frac {9 \cos \sqrt {x}}{\sqrt {x}} \cdot \left( \sqrt {x} \right)^{\prime} ........by the second fundamental theorem of calculus

    \Rightarrow g'(x) = \frac {9}{2} \frac {\cos \sqrt {x}}{ \sqrt {x}} \cdot x^{- \frac {1}{2}}

    \Rightarrow g'(x) = \frac {9 \cos \sqrt {x}}{2x}


    EDIT: Ah, beaten by the great qbkr21!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The Fundamental Theorem of Calculus
    Posted in the Calculus Forum
    Replies: 10
    Last Post: November 17th 2008, 03:48 PM
  2. Fundamental Theorem of Calculus
    Posted in the Calculus Forum
    Replies: 11
    Last Post: June 6th 2008, 12:29 PM
  3. Fundamental Theorem of Calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2008, 08:53 PM
  4. Replies: 2
    Last Post: June 14th 2007, 06:35 AM
  5. fundamental theorem of calculus
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 23rd 2006, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum