Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and the given lines. y=x^.5 , y=0 , x=4. revolove arond the line x=4

Answer 1

Your element of volume will be\[dV=2\pi(4-x)y{dx}\]using the cylindrical shells method. Substituting y=x^(1/2), and integrating, you have\[V=\int\limits_{0}^{4} 2\pi(4-x)x^{1/2}dx\]\[={2\pi}\int\limits_{0}^{4}4x^{1/2}-x^{3/2}dx \]and you can take it from here...