Question 1. Find the length of the curve specified by the given function over the given interval. y = x2/3 from (1, 1) to (8, 4)Question 2. Find the surface area of the object generated when the following curve revolves around the sisaxis. yzfrommzZtowz. Question 3. Find the surface area of the object generated when the following curve revolves around the yaxis. yzxg/Efromwzltow:27. Question 4. A thin stretched wire that is 1 meter long has a density function of p(ac) : sin(27r:c) | 2 kg/m, Where :r = 0 corresponds to the left end of the Wire. Where does the Wire have maximal density? What the mass of the Wire? Question 5. You are at Home Depot and see that a certain lightbulb has an average lifetime of 1,000 hours. You decide to model the failure probability of these lightbulbs as an exponential density function with mean ,u = 1000. (a) What is the probability that the light bulb burns out in 500 hours? (b) If you need the bulb to last 1,200 hours, what is the probability that a bulb meets that goal? (0) In what ways is the exponential density function an unrealistic model for describing the lifetime of a lightbulb? Question 6. Consider the function f(:c) : l/w on the interval QC 2 1 for the following problems. (a) Sketch the solid obtained by revolving the curve y = f (.93) about the maxis for m 2 1. How would you roughly describe the shape? (b) Find the volume of this object. You will have to correctly formulate an improper integral. (0) Find the surface area of the same object. You will have to correctly formulate an improper integral. (d) Carefully consider your answers to parts (b) and (c). Are they consistent with each other? Do they contradict each other? Explain your reasoning