Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper

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

    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

    $$\int_0^{x^2} \! \sqrt{t^4+x^3} \, \mathop{dt}=\mathop{I}(0,x^2,x^3)$$
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook