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Integral using Chain Rule

  1. Jul 18, 2013 #1
    how do I find the integral of ∫√(t^4+x^3)dt from 0 to x^2?
     
  2. jcsd
  3. Jul 18, 2013 #2

    lurflurf

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    $$\int_0^{x^2} \! \sqrt{t^4+x^3} \, \mathop{dt}$$

    unless x depends on t treat it as a constant inside the integral
    find


    $$\mathop{I}(a,b,C)=\int_a^{b} \! \sqrt{t^4+C} \, \mathop{dt}$$

    (note this is an eliptic integral)
    then

    $$\int_0^{x^2} \! \sqrt{t^4+x^3} \, \mathop{dt}=\mathop{I}(0,x^2,x^3)$$
     
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