The current in a coil of self inductance \( 2.0 \, \text{H} \) is increasing according to \( I = 2 \sin(t^2) \, \text{A} \). The amount of energy spent during the period when current changes from \( 0 \) to \( 2 \, \text{A} \) is __________ \( \text{J} \).
