In this lesson, we will learn how to find the volume of a solid generated by revolving a region around either a horizontal or a vertical line using integration.
Students will be able to
Q1:
Find the volume of the solid obtained by rotating the region bounded by the curves 𝑦=4+𝑥sec and 𝑦=6 about 𝑦=4 where 𝑥∈−𝜋2,𝜋2. Give your answer to two decimal places.
Q2:
Consider the region bounded by the curve 𝑦=34𝑥cos and the lines 𝑦=0, 𝑥=−𝜋8, and 𝑥=𝜋8. Set up an integral for the volume of the solid obtained by rotating that region about 𝑦=4.
Q3:
Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve 𝑦=𝑒 and the lines 𝑦=0, 𝑥=−5, and 𝑥=5 about 𝑦=−5.
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