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Integrate the following using the formula below: 

Find the exact length of the curve 

Two-part Question:  a) State the three conditions required to use the Alternating Series Test.   b) Show whether the series converges or diverges.   

Integrate the following using the formula below:  

Find the exact surface area of the resulting surface on the interval [0, 3] rotated about the x-axis.

Part 1: Explain how you would evaluate

Suppose a spring in equilibrium is 80cm long and a force of 2 Newtons (N) stretches the spring to a length of 1.2 meters. How much work is done by the spring force in stretching it from equilibrium to 3 meters?

Suppose 5 Joules (J) of work is required to stretch a spring from its natural length of 20 cm to 25 cm. How much work is needed to stretch the spring an additional 5cm?

Find the volume of the solid generated by revolving the region bounded by   and   about the line  .

Find the volume of the solid generated by revolving the region bounded by  and  about the x – axis.