Question: the 4 exercise will be on file please Use the washer method to nd the volume of the solid generated by revolving the region bounded

the 4 exercise will be on file please

Use the washer method to nd the volume of the solid generated by revolving the region bounded by y = 8x and y 2 4x2 about the xaxis. Use the shell method to find the volume of the solid generated by revolving the region bounded by 8 y = ,x =1, and y = 2 about the horizontal line y = 1. (Give an exact value leaving I? and any x natural logarithms.) Suppose that 4 Joules (J) of work is needed to stretch a spring from its natural length of 24 cm to a length of 34 cm. How much work is needed to stretch the spring from 29 cm to 33 cm? (If necessary, round your answer to 2 decimal places.) Lifting problem: Avertically oriented cylindrical tank with a radius of 2 meters and a height of 8 meters is half full of water. Letting y = 0 correspond to the bottom of the tank, nd the work required to pump the water to the top of the tank. The density of water p =1000% and gravity g z 9.81%. Express the answer in Newton-meters (N-m) or Joules (J)

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