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Math Help - fundamental theorem of calculus

  1. #1
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    fundamental theorem of calculus

    fundamental theorem of calculus

    find an expression for g(x)= integral from 0 to x of f(x)dx similar to the one for f(x).

    f(x) = x+3 for x less than or equal to -1
    f(x) = x^2 +1 for x > -1

    g(x)= integral from 0 to x of f(x)dx
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  2. #2
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    Quote Originally Posted by cm3pyro View Post
    fundamental theorem of calculus

    find an expression for g(x)= integral from 0 to x of f(x)dx similar to the one for f(x).

    f(x) = x+3 for x less than or equal to -1
    f(x) = x^2 +1 for x > -1

    g(x)= integral from 0 to x of f(x)dx

    Looks straight forward. If -1\le x, g(x)= \int_0^x f(t)dt= \int t^2+ 1 dt= \frac{x^3}{3}+ x. If x< -1 g(x)= \int_0^x f(t)dt = \int_0^-1 t^2+ 1 dt+ \int_{-1}^x t+ 3 dt = -\frac{4}{3}+ \int_{-1}^x t+ 3 dt = -4/3+ \frac{x^2}{2}+ 3x- \frac{7}{2}
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  3. #3
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    for the second function, x>-1

    you said, x<-1

    will this change my answer?
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  4. #4
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    find an expression for g(x)= \int_0^x f(x)dx similar to the one for f(x).

    f(x) = x+3 for x \le -1
    f(x) = x^2 +1 for x > -1

    g(x)= \int_0^x f(x)dx
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  5. #5
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    still need help with this problem, the above poster was incorrect. He switched up the functions and the bounds.. please help
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