Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

I've managed to confuse myself with a simple change of variables.

I have an integral of the form:

$$

I = \int_f^{\infty} dt \int_0^1 ds\, t\, F(t(1-s),ts),

$$

where $F(a,b)$ is some well behaved function and $f$ is a positive number. I want to change variables:

$$

x = t(1-s), \qquad y = ts,

$$

in terms of which the integral reads:

$$

I = \int_{x_i}^{x_f} dx \int_{y_i}^{y_f} dy\, F(x,y).

$$

I would naively conclude that:

$$

x_i=y_i=0,\qquad x_f=y_f=\infty,

$$

but this must be wrong because it is independent of f!

My question is: what are the limits of integration in the new variables and why?

Thanks in advance!

Wakabaloola

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Pesky change of variables in integral

Loading...

Similar Threads - Pesky change variables | Date |
---|---|

I dx as a small change in x | Tuesday at 8:17 PM |

I Rate of change of area under curve f(x) = f(x) | Jan 2, 2018 |

I Function of 2 variables, max/min test, D=0 and linear dependence | Dec 19, 2017 |

**Physics Forums - The Fusion of Science and Community**