(i) [math]\int_{a}^{\infty}{f\left(x\right)} \text{d}x = \lim_{b \to \infty} \int_{a}^{b}({f\left(x\right)}\text{d}x[/math] [br] (ii) [math]\int_{-\infty}^{b}{f\left(x\right)} \text{d}x = \lim_{a \to -\infty} \int_{a}^{b}{f\left(x\right)}\text{d}x[/math] [br](iii) [math]\int_{-\infty}^{\infty}{f\left(x\right)} \text{d}x = \int_{-\infty}^{0}{f\left(x\right)} \text{d}x + \int_0^{\infty}{f\left(x\right)} \text{d}x [/math]