what is the volume of the solid generated when the region bounded by the curve y^3=x^3 and the x-axis, is revolved about the x-axis. (use cylindrical shell method)
The volume of the solid generated when the region bounded by the curve y^3=x^3 and the x-axis is revolved about the x-axis can be calculated using cylindrical shells method. In order to calculate this volume, we must first find out what interval of revolution there is. Since the equation is y^3 = x^3, after taking cube root on both sides we get y = ±√x. Therefore, since we are revolving around the x-axis (y axis constant) from -∞ to +∞ in range of 0≤x≤1, for each value of ‘x’ within this range we will have two values y as stated above & thus making total interval 2.
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