A parabolic reflector is formed by rotating that part of the curve \[y = +\sqrt{x}\] which lies between x = 0 and x = 1 about the x-axis. a) Find the surface area of the reflector. b) Find the volume of revolution of the solid generated by revolving the curve about the x-axis between 0 and 1. c)Show that the length of the arc of the curve between 0 and 1 is: \[L={{1 \over 2} {\sqrt{5} + {\cosh ^{-1} \sqrt{5}} \over {2}}}\]

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A parabolic reflector is formed by rotating that part of the curve \[y = +\sqrt{x}\] which lies between x = 0 and x = 1 about the x-axis. a) Find the surface area of the reflector. b) Find the volume of revolution of the solid generated by revolving the curve about the x-axis between 0 and 1. c)Show that the length of the arc of the curve between 0 and 1 is: \[L={{1 \over 2} {\sqrt{5} + {\cosh ^{-1} \sqrt{5}} \over {2}}}\]

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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whats the surface area formula? integral 2pi sqrt ( 1 + f'(x)) ^2

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