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Multi-part problem for the conic section 

Find the exact surface area of the resulting surface on the interval [1, 2] rotated about the x-axis.

Find the centroid of the region bounded by the curves

Find the exact sum of the following series.   

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