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). y = 1 x 1/2 - x/2, 0 x 1 1/2 3/2 - Find the surface area of the bulb and use the result to approximate the amount of glass needed to make the bulb. Assume that the thickness of the glass is 0.015 inch. (a) Write the definite integral for finding the surface area of the bulb. 1/3 2 dx (b) Explain why the integral does not satisfy the definition of a definite integral. The integrand is not defined at x = 0. The integrand is not differentiable at x = 0. The integrand is not defined at x = +4 The integrand is not differentiable at x = (c) Use the integration capabilities of a graphing utility to approximate the surface area (in ft). (Round your answer to four decimal places.) ft2 (d) Approximate the amount of glass (in ft) needed to make the bulb. (Round your answer to five decimal places.) ft3