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Math Help - Can someone explain this integral?

  1. #1
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    Can someone explain this integral?

    Hi,
    I have the following step in a derivation

    \lambda^2 \cdot \exp{(-\lambda w)} \int_{0}^{w} \mathrm{d} x = \lambda^2 \cdot w \cdot \exp{(-\lambda w)}

    where w \geq 0 and x \geq 0 and w = x + y

    Whats going on here? Is the integral over w w.r.t. x w by definition? How can you have an integral over no function?

    I guess this is pretty school-ish, but I haven't seen it before and would appreciate any clarity that can be provided.

    Thanks, MD
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  2. #2
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    Re: Can someone explain this integral?

    The integral is just x|_0^w=w-0=w.
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  3. #3
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    Re: Can someone explain this integral?

    Hi and thanks for your reply. I see what you are saying I think, but if that is so, what is the difference between

    \int_0^w 1 \ \mathrm{d} x


    and


    \int_0^w \mathrm{d} x


    ?

    Are these equivalent?

    Thanks again for your time. MD
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  4. #4
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    Re: Can someone explain this integral?

    Yes, they are equivalent.
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