Evaluate the integral by reversing the order of integration of e^x^2 ?

Integral 0 to 1 and integral from 8y to 8 of e^x^2 dx dy!

thanks,

2 Answers

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  • Dave
    Lv 6
    7 years ago
    Favorite Answer

    Region of integration: http://www.wolframalpha.com/input/?i=x%E2%89%A58y%...

    ∫(y=0 to 1) ∫(x=8y to 8) e^(x²) dx dy

    Becomes

    ∫(x=0 to 8) ∫(y=0 to x/8) e^(x²) dy dx

    ∫(x=0 to 8) x/8e^(x²) dx

    1/16 ∫(x=0 to 8) 2xe^(x²) dx

    1/16 e^(x²) [0 8]

    1/16 [e^(64) - 1]

  • Eliot
    Lv 5
    7 years ago

    You need to sketch the limits in the xy plane to do this. You get

    ∫ ∫ e^(x²) dy dx.....over y = [0 to x/8] and x = [0 to 1]

    This is easy to do now so I'll leave you to it.

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