Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. f(x)=3eX1;[3,5] E} The area between the xaxis and f(x) is El. (Do not round until the final answer. Then round to three decimal places as needed.) 5 Pollution from a factory is entering a lake. The rate of concentration of the pollutant at time t is given by P'(t)= 70t2 where t is the number of years since the factory started introducing pollutants into the lake. Ecologists estimate that the lake can accept a total level of pollution of 4850 units before all fish life in the lake ends. Can the factory operate for 5 years without killing all the fish in the lake? I E> Set up the definite integral that gives the total pollutant concentration in the lake after 5 years. D [Ddt D Can the factory operate for 5 years without killing all the fish in the lake? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Do not round until the final answer. Then round to the nearest whole number as needed.) 4:} - The company can operate for 5 years without killing all the fish in the lake since there will be only units of pollution in the lake. B- The company cannot operate for 5 years without killing all the fish in the lake since there will be units of pollution in the lake. Pollution begins to enter a lake at time t= 0 at a rate (in gallons per hour) given by the formula f(t), where t is the time (in hours). At the same time, a pollution filter begins to remove the pollution at a rate g(t) as long as the pollution remains in the lake. f(t)=12(1 -e_0'5t) , g(t) = 0.7t ~E> a. How much pollution is in the lake after 11 hours? The amount of pollution that remains in the lake after 11 hours is D gallons. (Do not round until the final answer. Then round to the nearest hundredth as needed.) b. Use a graphing calculator to find the time after t = 0 when the rate that pollution enters the lake equals the rate the pollution is removed. The rate of pollution entering equals the rate of the pollution being removed after B hours. (Round to the nearest whole number as needed.) c. Find the amount of pollution in the lake at the time found in part b. The amount of pollution in the lake after 17 hours is approximately |:| gallons. (Do not round until the final answer. Then round to the nearest hundredth as needed.) 0]. Use a graphing calculator to find the time when all the pollution has been removed from the lake. The time when all the pollution has been removed from the lake is D hours. (Round to the nearest hundredth as needed.)