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In this lesson, we will learn how to find the volume of a solid by revolution of a two-dimensional region about the x-axis using the disk method.
Q1:
Consider the region bounded by the curve π¦ = 5 π β 2 π₯ 2 and the lines π¦ = 0 , π₯ = β 4 , and π₯ = 4 . Set up an integral for the volume of the solid obtained by rotating this region about the π₯ -axis.
Q2:
Consider the region bounded by the curve π¦ = 4 π β 5 π₯ 2 and the lines π¦ = 0 , π₯ = β 1 , and π₯ = 1 . Set up an integral for the volume of the solid obtained by rotating this region about the π₯ -axis.
Q3:
Consider the region bounded by the curve π¦ = 3 3 π₯ c o s 2 and the lines π¦ = 0 , π₯ = β π 6 , and π₯ = π 6 . Set up an integral for the volume of the solid obtained by rotating this region about the π₯ -axis.
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