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:
$$L={{1 \over 2} {\sqrt{5} + {\cosh ^{-1} \sqrt{5}} \over {2}}}$$

Question

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:
$$L={{1 \over 2}  {\sqrt{5} + {\cosh ^{-1} \sqrt{5}} \over {2}}}$$

perl · Answer

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