1) Consider the region bounded by the functions y = and y = -x2 + 7, where the functions intersect at the points (1,6) and (2,3), and where y -x2 + 7 is the top and right-most 6 function in the bounded region, which means that y = is the bottom and left-most function in the bounded region

1) Consider the region bounded by the functions y = and y = -x2 + 7, where the functions intersect at the points (1,6) and (2,3), and where y -x2 + 7 is the top and right-most 6 function in the bounded region, which means that y = is the bottom and left-most function in the bounded region. Calculate the volume of the solid generated by revolving the region about the line y = 7 using the Cylindrical Shell Method (we now know from the last quiz that the answer is n [394 – 84 In 2]): x 2. Find the arclength of the following curve: Function: X= g(y) = syvt +1 dt Bounds: 0 = y < 3. Hint: Since x = g(y) is defined as an integral, and you need g'(y) for the arclength formula, use the Fundamental Theorem of Calculus Part I to find g'(y). 1. Consider the function y = &x)/s from x = 0 to x = (3/2) revolved about the x-axis. (a) Set up, but do not evaluate, the integral required to calculate the surface area in terms of x: (b) Set up, and this time evaluate, the integral required to calculate the surface area in terms of y: 2. Using Hooke's Law: It took 1800 Joules of work to stretch a spring from its natural length of 2 m to a length of 5 m. Find the spring's force constant.