Assignment:
For the following problem, sketch the region and then find the volume of the solid where the base is the given region and which has the property that each cross-section perpendicular to the x-axis is a semicircle.
1) The region bounded above by y=cosx, below by y=sinx and on the left by the y-axis
For the following problem, find the volume of the solid formed when the region described is revolved about the x-axis using washers or disks.
1) The region bounded by the lines x=0, x=1, y=x+1, and y=x+2
For the following problem, use shell to find the volume of the solid formed by revolving the given region about the y-axis.
1) The region bounded by the curve y= , the y-axis and the line y=1.
2) The region inside the ellipse about the y-axis.
Provide complete and step by step solution for the question and show calculations and use formulas.