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Math Help - how to integrate?

  1. #1
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    how to integrate?

    If a function f is defined by f(x) = S from 0 to x (1 / (1 + t^4)) dt, is f(1) = to 1/2?

    I take it I have to integrate that thing, how do I do it?
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  2. #2
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    Quote Originally Posted by LeoBloom. View Post
    If a function f is defined by f(x) = S from 0 to x (1 / (1 + t^4)) dt, is f(1) = to 1/2?

    I take it I have to integrate that thing, how do I do it?
    we can say no without actually evaluating the integral.

    f(1)=\int_{0}^{1}\frac{1}{1+t^4}dt > \frac{1}{2}

    By camparison the minimum of \frac{1}{1+t^4} on [0,1] is 1/2 and the max is 1 so

    \int_{0}^{1}\frac{1}{2}dt < \int_{0}^{1}\frac{1}{1+t^4}dt < \int_{0}^{1}1dt

    equallity could only happen if the integrand was constant on [0,1]

    I hope this helps.

    Good luck.
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  3. #3
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    Nope, sorry I didn't follow. I dont see how you get a min of 1/2 and a max of 1.
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  4. #4
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    Quote Originally Posted by LeoBloom. View Post
    Nope, sorry I didn't follow. I dont see how you get a min of 1/2 and a max of 1.
    let

    h(t)=\frac{1}{1+t^4}

    h(0)=\frac{1}{1+0^4}=1

    h(1)=\frac{1}{1+1^4}=\frac{1}{2}

    If your really want to be rigorous you could verify this with the first and second derivative test, but the function is postitive and decreasing for all t > 0 so its max is at the left end point and its min is at the right end point.

    I hope this clears it up.
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