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Math Help - equation of curve that is a concatenation of sections of two curves

  1. #1
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    equation of curve that is a concatenation of sections of two curves

    just need to verify this.
    if a have a function f(x) and a function g(x) and the area under f(x)
    from a known a to a variable x is (integral from a to x of)f(x);
    let f1(x)= (integral from a to x of)f(x);
    and
    the area under g(x) from the same variable x to a known b is
    (integral from x to b of)g(x)
    let g1(x)=(integral from x to b of)g(x);
    now let c(x)= f1(x)+g1(x);
    first isnt c the area of the two regions
    and isnt
    c'(x)(the derivative of c) the function of the curve above the two
    regions(i.e region under f1(x) and region under g1(x))
    between a and b?
    Or at least if the function of the curve above the two
    regions(i.e region under f1(x) and region under g1(x))
    is fn(x)
    isnt fn(b)=c'(b);
    by second fundamental theorem of calculus
    would be greatful for any reply.thanks
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  2. #2
    MHF Contributor

    Joined
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    Quote Originally Posted by dynamo View Post
    just need to verify this.
    if a have a function f(x) and a function g(x) and the area under f(x)
    from a known a to a variable x is (integral from a to x of)f(x);
    let f1(x)= (integral from a to x of)f(x);
    and
    the area under g(x) from the same variable x to a known b is
    (integral from x to b of)g(x)
    let g1(x)=(integral from x to b of)g(x);
    now let c(x)= f1(x)+g1(x);
    first isnt c the area of the two regions
    Yes.

    and isnt
    c'(x)(the derivative of c) the function of the curve above the two
    regions(i.e region under f1(x) and region under g1(x))
    between a and b?
    Yes.

    Or at least if the function of the curve above the two
    regions(i.e region under f1(x) and region under g1(x))
    is fn(x)
    isnt fn(b)=c'(b);
    by second fundamental theorem of calculus
    would be greatful for any reply.thanks
    Yes, to all of those questions.
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  3. #3
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    Joined
    Feb 2009
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    Quote Originally Posted by HallsofIvy View Post
    Yes.


    Yes.


    Yes, to all of those questions.
    thank you so much for replying to this question.This is very important to me but i have to ask another question.Are you absolutely sure beyond all possible doubt?!!in
    fn(b)=c'(b);
    b is from here
    let g1(x)=(integral from x to b of)g(x);
    just need to be absolutely sure.Thanks again.
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