If g(x)=∑n=0∞(−1)nx2n2n(n!)2g(x) = \sum_{n=0}^{\infty} (-1)^n \frac{x^{2n}}{2^n (n!)^2}g(x)=∑n=0∞(−1)n2n(n!)2x2n, what is ∫01g(x) dx\int_0^1 g(x) \, dx∫01g(x)dx in terms of a known function? (Choose the closest match.)
J0(1)J_0(1)J0(1) (Bessel function)
sin(1)\sin(1)sin(1)
cos(1)\cos(1)cos(1)
e1/2e^{1/2}e1/2