\f\fEvaluate the definite integral. 3 5U _ 1 = - [3 (\"+4)2] du |:| (Type an exact answer in terms of e.) Evaluate the definite integral. W / A 3x NX + 9 dx O 8 W / - W / A 3x V X + 9 dx = O (Type an exact answer, using radicals as needed.)Use the definite integral to nd the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the xaxis in the given interval. f(x) = 75 - 3x2; [0,8] For the interval [0,8] the area between the x-axis and f(x) is E. (Type an integer or a simplied fraction.) 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 ) = 2 [1,e3 ] (. . . The area is (Type an exact answer in simplified form.)The graph of f(x), shown here, consists of two straight line segments and two quarter circles. Find 16 + the value of f( x) dx. X 2 16 16 O1 3 A small company of science writers found that its rate of prot (in thousands of dollars) aftert years of operation is given by P'(t) = (3t+ 6)(t2 + 4t + 3) . (a) Find the total profit in the rst three years. (b) Find the prot in the seventh year of operation. (c) What is happening to the annual profit over the long run? (a) The total prot in the first three years is $|:|. (Round to the nearest dollar as needed.)