3.1. Determine the area determined by the function f(x) = 5x3 + 2x2-3x and the lines x = -1 and x=1 3.2. Calculates the region between the curvey=+2.0sxs 12 and the x-axis is rotated about the x-axis to generate a solid. Find the Volume of Revolution. 3.2.2. Find the volume of the solid of revolution given by y = 100 -x+3 and the x-axis (0 Sxs 8) around the y-axis. 3.2.3. Obtain the volume of the solid represented by y = 219-x and the axes on the first quadrant. 3.3. Find the arc length of the 5yz = x3-5 included in x = 3 and x = 10. 3.4.1. A force of 125 N is required to support a shock absorber on a certain machine from its natural position of 40 cm to a length of 75 cm. How much work is done in stretching the shock absorber from 75 cm to 135 cm? 3.4.2. The gate to evacuate the water in a vertical dam has the form shown in the figure. If the top of the gate is at a depth of 4 meters from the water surface. Calculate the force exerted by the water over the gate. 4 m 3 m 2 m