In a 1995 study of the effects of low-dose aspirin, subjects were given one 80 mg dose of acetylsalicylic acid (ASA). The concentration C(t) (in μg/mL) of ASA in the bloodstream after t hours was modeled by the function:
C(t) = 32t^2e^(-4.2t)
In pharmacokinetics, the integral ∫0 to T C(t)dt is called the AUC (which stands for "area under the curve"). The AUC is used to determine the bioavailability of the drug in the body, which is a measure of how much of the drug is available in the system to produce a biological effect. Find the AUC of C(t) for T = 1.