Question

(Please answer all 3 questions and explain how you get the answer. thank you.)

Q1. A cable with mass 0.5 kilograms per meter (kg/m) is used to lift 150 kg of coal up a mine shaft 50 meters deep. Set up the integral that will calculate the work needed to lift the load one quarter of the way up the shaft. (Set up the integral only, no need to compute its value.)

Answer . work = .....

Q2. Determine the exact length of ? = 2/3 (? − 1)^(3/2), 1 ≤ ? ≤ 4. Don’t use your calculator to approximate your answer. Keep it exact.

Answer L = ........

Q3. Determine the exact area of the surface obtained by rotating ? = square room of (9-x^2) , −2 ≤ ? ≤ 2 about the x-axis.

Answer A =....

Answer 1