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Chapter 11: Q3P (page 548)

Prove that erf(x) is an odd function of x. Hint: Put t = -s in (9.1) .

Short Answer

Expert verified

It has been proved that the erf(x) is an off function of x .

Step by step solution

01

Definition of error of function

The error of the function is defined as (x)=2蟺鈭�0xe-t2dt.

02

Prove that error is odd

The value of integration is erf(x)=2蟺鈭�0xe-t2dt.

Substitute -x in place of x .

erf(-x)=2蟺鈭�0-xe-t2dt

Let u = -s , then du = -ds .

The equation becomes as follows:

erf(-x)=2蟺鈭�0xe-s2-dserf(-x)=-erf(x)

Hence, the statement has been proved.

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