A triple integral involving deltas

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SUMMARY

The discussion focuses on evaluating a triple integral involving delta functions, specifically the integral of the expression (x^2 + 32*z^2) * cos(y) * e^(x - 4*z) multiplied by delta(x - 1), delta(y - pi), and delta(z - 0.25). The participant concluded that the integral evaluates to zero due to the properties of the delta function, which results in the overall multiplication yielding zero when evaluated at the specified points. The participant also clarified their understanding of the delta function's role in integrals, confirming that it simplifies the evaluation process by collapsing the integral to the function's value at the delta's argument.

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skrtic
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SOLVED

Homework Statement


evaluate the intergral

Homework Equations

sorry about how this is going to look don't know the language to display nicely and wouldn't take my copy and pasteall integrals are form -infinity to infinity

(x^2+32*z^2)*cos(y)*e^(x-4*z) delta(x-1) delta (y-pi) delta(z-.25) dx, dy dz

The Attempt at a Solution

well i looked at just the cos(y) part and got sin(y) then for the delta i plugged in pi since it is zero elsewhere and that gives me a 0 overall and since it is all mulitplication that makes the whole integral o?

thats my take.

never really understood the delta's in integrals
 
Last edited:
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\int_{-\infty}^{+\infty}dx\,f(x)\delta(x-a) = f(a)
 
ok. that makes sense. and kinda looks familiar now that i see it and makes the problem a little better.

thanks
 

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