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Limit with integrals problem

  1. Jul 7, 2013 #1
    [itex]lim_{x\rightarrow + ∞} \frac{\int^{x^3}_{0} e^{t^2}dt}{x \int^{x^2}_{0} e^{t^2}dt} [/itex]

    Attempt at a solution: I don't really know where to start. Any hints?
  2. jcsd
  3. Jul 7, 2013 #2


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    Homework Helper

    L' Hopital's Rule. Product Rule for the denominator. Fundamental Theorem of Calculus to differentiate the integrals. Don't forget that the bounds are functions of ##x##, so apply Chain Rule (Leibniz's Rule).

    After the first step, you'll end up with an expression that I'll call ##L##. Find and simplify ##L^{-1}## with a further application of all those rules. Then deduce what ##L## should be at the limit.
    Last edited: Jul 7, 2013
  4. Jul 7, 2013 #3
    Thanks. When I get home I'll get to work.
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