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Just evaluate the function where the value passed to the delta is 0. i.e. if your are trying to integrate x^2*delta(x-3)dx, that is just equal to the value of x^2=3^2=9 since x-3=0 at x=3. If the limits of integration do not include the value where delta is 0, then the integral is 0 since delta(x)=0 everywhere that x is not=0.
Thinking of it from a graphical perspective, you are asking for the area under the curve of a function multiplied by the delta function, which just leaves the portion of the graph at where the spike from delta happens. Everywhere else, the graph is 0. So the only thing that contributes to the integral is the value of the function where delta(0) happens. Since the integral of the function at that point is constant and delta at that point is just 1, it's just the value of the function at that point.
I do not believe there is a delta function in the TI-NSpire for you to do this directly. You need to recognized the meaning of the delta function.
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