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Math Help - Study help ASAP with a few problems (Laplace, areas, an integral)

  1. #1
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    Study help ASAP with a few problems (Laplace, areas, an integral)

    1) Let W be the region bounded by the curve y=e^(-x^2) and the x-axis, x is greater or equal to 0. Show that W has finite area when A = .5 sqrt(pi). Then calculate the volume generated by revolving W about the y-axis.

    2) f(x)=1/(sqrt(2pi)) * integral from negative infinity to x of: e^[(-t^2)/2] dt
    Prove that this integral on the right converse for all real x

    3) The Laplace transform of f is the function F defined by setting:
    F(s) = integral from 0 to infinity of: e^(-sx) f(x)dx
    The domain of F is the set of numbers s for which the improper integral converges. Find the Laplace transform F of f(x)=1 specifying the domain of F.

    Thanks for the help!
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    Quote Originally Posted by jgall View Post
    1) Let W be the region bounded by the curve y=e^(-x^2) and the x-axis, x is greater or equal to 0. Show that W has finite area when A = .5 sqrt(pi). Then calculate the volume generated by revolving W about the y-axis.
    What does A have to do with this integral?? This question makes no sense as stated.

    -Dan
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  3. #3
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    I think that it just means A is the area of the curve, and A = .5 sqrt pi
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