please include all steps necessary for each question

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A. graphing calculator is required for this problem, Let R and S be the regions in the rst quadrant shown In the gure. The region R is bounded by the xaxis and the graph ofy: 25m. The region Sis bounded by the y-axis and the graphs ofy : 3 2x and y : 2sinx. Part A: Find the area of S. (15 points) Part E: Find the volume of the solid generated when R is revolved about the xaxls. {15 points) Part c: Write, but do not evaluate, an integral expression that can be used to find the volume of the solid when Sis revolved about the xaxis, (10 points) For the regions bounded by y = 6cosx and y = X 2-7. Part A: Find the limits of integration. (10 points) Part B: Write an expression representing the total area. (10 points) Part C: Solve for the total area. (10 points)A vovo is moving up and down a string so that its velocity at time t' is given by v(t) = 200s(t'] for time t2 I). The initial position of the yovo at time t: I) is x = 2. Part A: Find the average value of vm on the interval [0%]. {10 points) Part B: What is the displacement of the yovo from time t: D to time t: 11'? (10 points) Part C: Find the total distance the yeyo travels from time t = I) to time 2': TI'. (10 points)