Question

The error function, erf(x), is defined by the following

Answer 1

any idea how to go about this

Answer 2

Try plugging in the value for the first one and use the fundamental theorem of calculus for the second one.

Answer 3

ok give me a sec

Answer 4

got first one and the second one is tricky i don't exactly know how to go about it in regards to this error function would you mmd giving a bit of insight

Answer 5

Try to do this with a function you can integrate and it might become clear. I'll show you an example: \[\frac{d}{dx} \int\limits_0^x t^3 dt = \frac{d}{dx} \frac{1}{4}x^4=x^3\]

So essentially you are just removing the integral sign. You can go more in depth with it though, suppose the upper and lower bounds aren't simply a constant and x to the first power, then the chain rule comes in:

\[\frac{d}{dx} \int\limits_x^{x^2} t^3 dt = \frac{d}{dx} \frac{1}{4}(x^8-x^4)=2x^7-x^3\]