Solving a Difficult Double Integral: Tips and Tricks for Success

[madachi]

Homework Statement

\int_{0}^{1} \int_{0}^{1} \sqrt{4x^2 + 4y^2 + 1} dx\,dy

The Attempt at a Solution

This integral is tough for me, I couldn't think of a way to evaluate it. Can you suggest me the first step to do this problem?

Thanks!

 

[CompuChip]

The sum of squares strongly suggests a change to spherical coordinates (in 2D, that would be polar coordinates).

An integral like
\int r \sqrt{1 + r^2} \, dr
is easier, because r is the derivative of 1 + r².