102k views
3 votes
Find the volume of the solid obtained by rotating the region bounded by the curve f(x) = 2eˣ - 7, the x-axis, the y-axis, and the line x = 1 around the y-axis?

1 Answer

1 vote

Final answer:

To find the volume of the solid, use the method of cylindrical shells by integrating the volumes of vertical slices of the region.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the curve f(x) = 2eˣ - 7, the x-axis, the y-axis, and the line x = 1 around the y-axis, we can use the method of cylindrical shells. Cylindrical shells are formed by taking vertical slices of the region and rotating them around the y-axis. The volume of each shell can be approximated as the product of its height, circumference, and thickness. By integrating these volumes over the range of y-values, we can find the total volume of the solid.

User Motine
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories