The graph shown is f(x) = In (x + 2). What is the integral function g(t) that defines the area under this line between x = 0 and x = 3? NWA X 54 3 2/ 1 1 23 4 5 0 g(t) = S In(t + 2) dt O g(t) = [ In(t + 2) dt O g(t) = > In(t - 2) dt O g(t) = S In(t) dt + 2The graph shown below is f(x) = 3x2 - 2. If g(x) = So f(t) dt , what is g'(2)? AY 4+ X 54 3 2 141 2345 0 4 O 10 O 12 O 14What is the total change of f(x), if f'(x) = sin(4x), over the interval 0, ? O -1 O V2 2 O 0 O 1An object is moving along a horizontal path shown in the graph. What is the displacement of the object for the time interval [0, 5]? 0 Displacement is -3. 0 Displacement is 3. 0 Displacement is 7. 0 Displacement cannot be determined from the information given. A can is dripping out water at a rate of r(t) = , cm3/sec. If the can held 50 cm3 of water at time t = 1, what formula describes the amount of water remaining at time t = 3? Do not evaluate the integral. O v(3) = 50 - 3 51 2 dt O v(3) = 50 - Si 2 dt O v(3) =1 - Si 2 dt O v(3) = 50 + ST 1 dtTom is running a race. Between time t = 0 min and t = 10 min, his speed is 3 miles an hour; between time t = 10 min and t = 30 min, his speed is 5 miles an hour. How far has he run? 0 2.167 miles 0 2.833 miles 0 3miles O 3.5 miles \fIf f(x) = 3x + 2, which equation describes the average value of f(x) over the interval [1, 4]? O 4i1 f14(3:1: 2) da: 0 1'14 (313 7 2) d2: 1 4 4 O 4i1f1(3m+2}d:1