Understanding the Dirac Delta Function: Solving the Integral of Delta(x-b)

[extreme2000]

Q: Integral of Delta(x-b)dx and the lower limit is (-) infinity and upper is a
Please help me in steps tried my best to solve.Note this is not homework I was doing the book problems or my practice
Thanks

 

[AiRAVATA]

What can you tell if $a<b$?

What about the integral in the whole line?

 

[extreme2000]

Integral Problem

Dear User
Actually I am sorry to say that my integration is little rusty that's why just I need the first step for this question,Please if you can give it to me
Thanks

 

[nicksauce]

Fact: $$\int_A\delta({x-b})dx=1 \textnormal{ if } b\in{A} \textnormal{ or } 0 \textnormal{ otherwise.}$$

That should be all the information you need. This fact should be fairly obvious to understand, but we can explain it in more detail if needed.