1. A car moves along a straight road in such a way that its velocity (in feet per second) at any time t (in seconds) is given by v(t) = 3t v16 - t2 for 0 S t S 4. Find the distance traveled by the car (in feet) in the first four seconds (from t = 0 to t = 4). Round your final answer to two decimal places if needed. 2. Use a Riemann Sum to approximate the area under the graph of f (x) = 3x + 2 and above the x-axis from x = 1 to x = 5 using three rectangles and a. Left endpoints b. Right endpoints C. Now average your answers from (a) and (b).3. Sketch the graph of f(x) = 3x + 2 and shade the area between f(x) and the x-axis from x = 1 to x = 5. Use an integral to find the exact area of the region you shaded. (Is this close to your answer from #2c?) 4. Evaluate each definite integral. Leave your answers exact unless otherwise stated. [ y(2y2 - 3)5 dy 2 (2x - 7)2 dx j ( Avr - 3 v7 ) derFind the following integrals. Leave your answers exact. 5 ( In x dx X 6. x Inx dx 7. 5xe3x dx 8. Use the definite integral to find the area between the x-axis and f (x) = 4 - x on the interval [2, 4]. Start with a graph of the function and shade the area you are looking for