Find the arc length of y = 2 ln(cos 1/2x) on [0, pi /2]. Your final answer must

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Find the arc length of y = 2 ln(cos 1/2x) on [0, pi /2]. Your final answer must be in exact form (no decimal approximations!). Write out Simpson's Rule with n = 6 for the following integral. Each term should be in exact form, but you do not need to compute a final value once all the terms are written out. A bowl is formed by revolving the lower half of the ellipse x2/4 + (y - 1)2 = 1 around the y-axis. A lead sphere of diameter 1 is dropped in the bowl and settles to the bottom, then the bowl is filled with water. Write the expression that would give the total volume of water in the bowl. (You can use Maple or a calculator to plot the ellipse.)

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