Results 1 to 5 of 5

Math Help - fundamental theorem

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    139

    Unhappy fundamental theorem

    let F(x)= int from 1 to x of (e^t)/(2t+3)
    which is the equation of the tangent line to the graph of F(x) at x=1?
    I can't find the F(x0) since I don't know how to solve that integer. Might someone help me?thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by 0123 View Post
    let F(x)= int from 1 to x of (e^t)/(2t+3)
    which is the equation of the tangent line to the graph of F(x) at x=1?
    I can't find the F(x0) since I don't know how to solve that integer. Might someone help me?thanks
    Fundamental theorem of calculus may be written as:

    <br />
\frac{d}{dx}\ \int_a^x f(t)\ dt=f(x)<br />

    so:

    <br />
\frac{dF}{dx}(x)=(e^x)/(2x+3)<br />

    So the slope of y=F(x) at x=1 is:

    <br />
\frac{dF}{dx}(1)=f(1)=(e^1)/(2+3)=e/5<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2006
    Posts
    139
    I got the idea of the slope. my problem comes when I need to solve the integer; I mean, since this is the equation y=m(x-x0)+y0, m is the slope, which is clear, and x0=1, I need to find y0 which is F(x) at x=1, and to do that I think I need to solve that integer, which I am not able to. I hope my explaination is clear enough...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by 0123 View Post
    I got the idea of the slope. my problem comes when I need to solve the integer; I mean, since this is the equation y=m(x-x0)+y0, m is the slope, which is clear, and x0=1, I need to find y0 which is F(x) at x=1, and to do that I think I need to solve that integer, which I am not able to. I hope my explaination is clear enough...

    <br />
F(x)= \int_1^x e^t/(2t+3)\ dt<br />

    so:

    <br />
F(1)= \int_1^1 e^t/(2t+3)\ dt=0<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2006
    Posts
    139
    now I see.. I mistook the very approach to the problem.. thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. fundamental theorem of cal
    Posted in the Calculus Forum
    Replies: 8
    Last Post: January 3rd 2009, 01:40 PM
  2. Second Fundamental Theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 12th 2007, 08:40 AM
  3. Fundamental theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 28th 2007, 12:40 PM
  4. Replies: 2
    Last Post: June 14th 2007, 06:35 AM
  5. fundamental theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 24th 2006, 05:44 AM

Search Tags


/mathhelpforum @mathhelpforum