Infinity Integral

When you get a Integral like this.

1. Definite Integral from a to infinite $\int _{a}^{\infty }f(x)\,dx$
2. Definite Integral from negative infinite to b $\int _{-\infty }^{b}f(x)\,dx$
3. Definite Integral from negative infinite to infinite $\int _{-\infty }^{\infty }f(x)\,dx$

you may will be confused by the infinite and ask a question how did I get the area of this. But you can think it as limit.

so you can transform it like this

1. Definite Integral from a to infinite $\int _{a}^{\infty }f(x)\,dx=\lim _{t\to \infty }\int _{a}^{t}f(x)\,dx$
2. Definite Integral from negative infinite to b $\int _{-\infty }^{b}f(x)\,dx=\lim _{t\to -\infty }\int _{t}^{b}f(x)\,dx$