Are you familiar with the laplace transform? If not, here is a walk through to get the reactance of a capacitor: For a capacitor i = C * dv/dt Therefore, v = 1/C * integral(i, 0 , t) + V0. Now the laplace transform is defined as follows I(s) = integral(i(t) * exp(-s*t), 0, inf) Now the cool thing is, if we integrate I(t) prior to performing the laplace transform we will get i2(t) = integral(i(t)) I2(s) = I(s)/s Applying this rule to our formula for v we get V(s) = 1/(C*s)*I(s). the reactance is just the imaginary part of the resistance of a component, therefore the reactance is: 1/(C*j*2*pi*f)
Whilst Santa is busy stuffing is, js and ks into next years christmas stockings it may be worth noting that the reactance is given by X = 1/2π f C i.e. = 1/(2πx400x2.2 x10) ohms The voltage rating of the capacitor or the applied voltage is immaterial.
bujak18, I think that what these guys wrote is as simple as it gets. They took the definition of capacitive reactance, plugged in your values and gave you the answer.