- #1

- 587

- 242

- Homework Statement
- Evaluate ∫∫ -4 / (1+ x^2 + y^2)^4 dx dy

- Relevant Equations
- ∫∫ -4 / (1+ x^2 + y^2)^4 dx dy

Dear all,

Last semester on the final exam, our professor gave us an integral that seems difficult to solve.

The integral came at the end of a lengthy problem, where we were asked to find the net Gauss curvature of Enneper's surface.

The integral that emerged is the following.

We tried substituting

which does not help.

We tried evaluating the following single integral to see if it simplifies.

...

And the calculations continue for another 3 pages and become more complicated.

The evaluated integral is the following.

We could integrate this expression with respect to y and evaluate the result from -∞ to ∞ .

The answer for the net curvature is

Is there a key integration technique we are missing?

This integral seems difficult to solve without using technology.

Thank you.

Last semester on the final exam, our professor gave us an integral that seems difficult to solve.

The integral came at the end of a lengthy problem, where we were asked to find the net Gauss curvature of Enneper's surface.

The integral that emerged is the following.

We tried substituting

*x = sinθ, y = cosΘ*and ended up withwhich does not help.

We tried evaluating the following single integral to see if it simplifies.

...

And the calculations continue for another 3 pages and become more complicated.

The evaluated integral is the following.

We could integrate this expression with respect to y and evaluate the result from -∞ to ∞ .

The answer for the net curvature is

*- 4π*in differential geometry textbooks.Is there a key integration technique we are missing?

This integral seems difficult to solve without using technology.

Thank you.