and the function y = 2x. Let R be the region bounded by the parabola y...

  

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and the function y = 2x. Let R be the region bounded by the parabola y = x (a) (2 points) Sketch the region R. (b) (4 points) Set up the integral to calculate the volume of the solid obtained by rotating the region R around the x-axis, and evaluate the integral. (c) (2 points) Set up the integral calculating the volume of the solid obtained by rotating the region R around the line y = 4. (d) (2 points) Set up the integral calculating the volume of the solid obtained by rotating the region R around the line x = -1. and the function y = 2x. Let R be the region bounded by the parabola y = x (a) (2 points) Sketch the region R. (b) (4 points) Set up the integral to calculate the volume of the solid obtained by rotating the region R around the x-axis, and evaluate the integral. (c) (2 points) Set up the integral calculating the volume of the solid obtained by rotating the region R around the line y = 4. (d) (2 points) Set up the integral calculating the volume of the solid obtained by rotating the region R around the line x = -1.