Finding the volume and surface area of a region bounded by curves.
Created by and copyright of Larry Perez. Funded by the state of California through Saddleback College. More information on videos, resources, and lessons at Algebra2Go.
Questions answered by this video:
How can you calculate the volume and surface area of an air intake manifold?
How can you find the area of the region bounded by the x-axis, lines x = ln (1/2), x = ln 2, and the curve f(x) = e^x?
How do you find the volume of the manifold generated by semicircular cross-sections whose radii is equal to the length of the partitions that are perpendicular to the x-axis and bounded between the x-axis and the function f(x) = e^x?
How do you find the intersection between the line x = ln2 and the curve f(x) = e^x?
How do you find the intersection between the line x = ln (1/2) and the curve f(x) = e^x?
What is the formula for the surface area of revolution?
How do you find the surface area of a curve rotated around the x-axis?
Staff Review
Currently 4.0/5 Stars.
This lesson solves a rather complicated problem of finding the volume and surface area of a region bounded by several lines and curves that is rotated around the x-axis to form an air intake manifold. This is a very applied problem with some very involved formulas and calculations in it.