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Math Help - integral of a square root

  1. #1
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    integral of a square root

    how do you find the integral of a square root of a polynomial?

    specifically,

    the integral of the sqaure root of (t^2+t^4)
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  2. #2
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    Quote Originally Posted by cottekr View Post
    how do you find the integral of a square root of a polynomial?

    specifically,

    the integral of the sqaure root of (t^2+t^4)
    \sqrt{t^2+t^4}=\sqrt{t^2(1+t^2)}=|t|\sqrt{1+t^2}


    We can find an antiderviative when t \ge 0 or when t < 0
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  3. #3
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    in the problem I have, its a definite integral from 0 to 1. but I'm not sure how to find the integral of anything under the square root
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  4. #4
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    Quote Originally Posted by cottekr View Post
    in the problem I have, its a definite integral from 0 to 1. but I'm not sure how to find the integral of anything under the square root
    \int_{0}^{1}t\sqrt{1+t^2}dt


    let u=1+t^2 \implies du=2tdt \iff \frac{1}{2}du=tdt

    \int_{1}^{2}\sqrt{u}\frac{1}{2}du=\frac{1}{2}\int_  {1}^{2}u^{1/2}du...
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