Flipping Limits in Integrals: Is it Valid?

[Kat007]

Hello,

Could you please tell me is it correct to say this:
If I have integral with lower limit of (x) and upper limit of (positive infinity), does it equal to
integral of lower limit (minus infinity) and upper limit (minus x)?

Do you know of any link to a website showing such a rule?

Thank you,

 

[Mark44]

Hello,

Could you please tell me is it correct to say this:
If I have integral with lower limit of (x) and upper limit of (positive infinity), does it equal to
integral of lower limit (minus infinity) and upper limit (minus x)?

Do you know of any link to a website showing such a rule?

Thank you,

In general, there's no such rule. However, if the integrand is an even function (i.e., f(-x) = f(x) for all real x), what you're asking about is true.

 

[Kat007]

Hi Mike,

Thank you, yes, this is the case. The integrand is the cdf of a standard normal with limits of a +ve constant on the bottom and positive infinity of the top. Then the limits flip and the signs also.

Thank you again!