Consider the region bounded by the curve y = (half of an ellipse) and the r-axis....

  

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Consider the region bounded by the curve y = (half of an ellipse) and the r-axis. a) Sketch the region, making sure to label the boundaries and intersection points clearly. b) Set up an integral to find the area of the region. Then evaluate this integral using integration techniques (do NOT give a geometric argument). c) Suppose the region is revolved around the r-axis to form a solid of revolution (called an ellipsoid). Set up an integral to find the volume of this solid. Then evaluate this integral using integration techniques (do NOT give a geometric argument). Consider the region bounded by the curve y = (half of an ellipse) and the r-axis. a) Sketch the region, making sure to label the boundaries and intersection points clearly. b) Set up an integral to find the area of the region. Then evaluate this integral using integration techniques (do NOT give a geometric argument). c) Suppose the region is revolved around the r-axis to form a solid of revolution (called an ellipsoid). Set up an integral to find the volume of this solid. Then evaluate this integral using integration techniques (do NOT give a geometric argument).