A triple integral involving deltas

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The integral involves evaluating (x^2 + 32z^2) * cos(y) * e^(x - 4z) with delta functions at specific points. The delta functions effectively reduce the integral to evaluating the function at those points, specifically at x=1, y=π, and z=0.25. The contributor notes that the cos(y) part leads to sin(y), which evaluates to zero when substituting y=π, resulting in an overall integral value of zero. There is also a mention of understanding delta functions better through the integral property that simplifies evaluations. The discussion concludes with an appreciation for the clarity gained regarding delta functions in integrals.
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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 teh delta's in integrals
 
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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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