Problem 1358 (difficulty: 4/10)

Give a function \(\displaystyle \varphi:[0,2]\to\R\) such that for any continuous function \(\displaystyle f:[0,1]\to\R\)

\(\displaystyle \int_0^1 \int_0^1 f(x^2+y^2) \dx \dy = \int_0^2 f \varphi. \)

Give me another random problem!