Find the volume of the solid generated by revolving the region bounded by the graphs of ( y=0, x=2 ), and ( y=x^{2} ) about the line ( y=-1 )

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Step:1 ：Set up the washer method for volume: ( V = pi int_{a}^{b} (R^{2}(x) - r^{2}(x)) dx )Step:2 ：Calculate the outer radius R(x) and inner radius r(x) based on the functions and line of revolutionStep:3 ：Evaluate the integral and find the volume: ( V = pi int_{0}^{2} (1 - (x^{2} + 1)^{2}) dx )

Answer

Step: 1 ：Set up the washer method for volume: ( V = pi int_{a}^{b} (R^{2}(x) - r^{2}(x)) dx )Step: 2 ：Calculate the outer radius R(x) and inner radius r(x) based on the functions and line of revolutionStep: 3 ：Evaluate the integral and find the volume: ( V = pi int_{0}^{2} (1 - (x^{2} + 1)^{2}) dx )

Find the volume of the solid generated by revolving the region bounded by the graphs of \( y=0, x=2 \), and \( y=x^{2} \) about the line \( y=-1 \)

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