Answer Happy

Write the definite integral for finding the indicated surface area. Then use the integration capabilities of a graphing utility to approximate the surface area. An ornamental light bulb is designed by revolving the graph of the equation shown below about the x-axis, where x and y are measured in feet (see figure). 1x1/2 - x³/2, 0≤x≤ y = : x≤ 1/3} Write the definite integral for finding the surface area (in ft²) of the bulb and approximate. (Round your answer to four decimal places.) 2π dx = ft² S Use the result to approximate the amount of glass needed to make the bulb (in ft³). (Assume that the glass is 0.015 inch thick. Round your answer to five decimal places.) V = ft³ y = ²x²¹/2²—x3³/2