# Integration of Q function

1. Jan 28, 2013

### myarram

can we simplify the below equation into another Q function?

∫0,4T(Q(2∏*(0.3) * ((t-5T/2)/(T√(ln2)))dt
where T is a constant

I have attached the equation in the attachements

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2. Jan 28, 2013

### Staff: Mentor

What is a Q function?

3. Jan 28, 2013

### myarram

4. Jan 29, 2013

### lurflurf

$$\int_0^x \mathrm{Q}(t) \, \mathrm{dt}=\frac{1}{2}\int_0^x \mathrm{erfc} \left( \frac{t}{\sqrt{2}} \right) \, \mathrm{dt}=\frac{1}{2} x \, \mathrm{erfc} \left(\frac{x}{\sqrt{2}}\right)+\frac{1}{\sqrt{2 \pi}}\left(1-e^{-x^2/2}\right)= x \, \mathrm{Q} \left( x \right)+\frac{1}{\sqrt{2 \pi}}\left(1-e^{-x^2/2}\right)$$
which can be shown by integration by parts
your integral can then be found by change of variable