An integral is given by \(\int_{-∞}^{∞} d x \int_{-∞}^{∞} d y \exp \left[-\left(x^2+y^2+2 a x y\right)\right]\), where a is a real parameter. The full range of values of $a$ for which the integral is finite, is
1
-∞ < a < ∞
2
-2 < a < 2
3
-1 < a < 1
4
-1 ≤ a ≤ 1