Use the Fundamental Theorem to evaluate the definite integral exactly. (6x2 + 6) dx Enter the exact answer. ( 612 + 6) dx = iUse the Fundamental Theorem to evaluate the definite integral exactly. 16 2 dx Enter the exact answer. 16 2 dx = 1Use the Fundamental Theorem to evaluate the definite integral exactly. 3x- dx = eTextbook and MediaUse the Fundamental Theorem to evaluate the definite integral exactly. + yo ) dy Enter the exact answer. + yo ) dy =Use the Fundamental Theorem to evaluate the definite integral exactly. 3 dx Enter the exact answer. 3 dx =Use the Fundamental Theorem to evaluate the definite integral exactly. 16 8 /x dx Enter the exact answer. 16 8 /x dx =If t is in years, and t = 0 is January 1, 2005, worldwide energy consumption, r, in quadrillion (1015) BTUs per year, is modeled by r = 462e0.019t (a) Write a definite integral for the total energy use between the start of 2005 and the start of 2016. Total energy used = dt quadrillion BTUs (b) Use the Fundamental Theorem of Calculus to evaluate the integral. NOTE: Round your answer to the nearest integer. Total energy used quadrillion BTUsCurrent Attempt in Progress At a time t hours after taking a tablet, the rate at which a drug is being eliminated is r(t) = 50(e-0.025t _ e-0.05t ) mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose. Enter the exact answer. The original dose was mg.The rate, r, at which people get sick during an epidemic of the u can be approximated by r = 1000te'0'5', Where a" is measured in people/dag,r and i; is measured in days since the start of the epidemic. (a) Write an improper integral, using the variable t, representing the total number of people that get sick. Total number gem-mg sick: f [:1a (b) Select the correct graph of r with a shaded area that represents the integral from part (a)