How Does the Delta Function Affect Integral Values?

mpouternot
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Homework Statement


I want to measure this integral ( Sd(x)δ(χ-c) , where c is constant
Thanks in advancE


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The Attempt at a Solution

 
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Do you mean
\int \delta(x-c)dx?

What is is the range of integration? Since you use the delta function, I assume you know how it is defined- immediately from the definition that integral is 1 if c is in the range of integration, 0 if not.

If you mean
\int_{-\infty}^x \delta(t-c)dt
That is the "Heaviside step function" H(x-c), equal to 0 if x< c, 1 if x\ge c.
 

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