When considering integration, how does one use the Heaviside function in order to alter the limits of integration. For example
If i have $$ \int_a^b f(x) dx $$ But want to change this integral to be over the range, for example $0$ to $\infty$, then how do i use the Heaviside to this?
From what i understand about graphing, H(x) is the line $y=1$ that begins at $0$ and goes to $+\infty$, or in this case $a$ to $b$.
$$\int_a^b{f(x)dx}=\int_a^{b}{f(x)[H(x-a)-H(x-b)]dx}=\int_0^{\infty}{f(x)[H(x-a)-H(x-b)]dx}$$