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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.