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Solution to the problem of the (previous) week
Problem:The neck of the bottle shown in the figure below is obtained by rotating
about the x-axis.
Determine the coefficients and find the area of the longitudinal section of the bottle and its volume bounded by the lines given in the drawing. Take the horizontal tangent lines at the x-coordinates 0 and into account.
(The results should be correct to three decimal places.)
Solution:First, we have
Finally, we obtain
The area is determined as follows:
The volume is determined as follows: