Solution Found!
Area and volume Consider the function f(x) = (9 + x2)–1/2
Chapter 4, Problem 59E(choose chapter or problem)
Area and volume Consider the function \(f(x)=\left(9+x^{2}\right)^{-1 / 2}\) and the region R on the interval [0,4] (see figure).
(a) Find the area of R.
(b) Find the volume of the solid generated when R is revolved about the x-axis.
(c) Find the volume of the solid generated when R is revolved about the y-axis.
Questions & Answers
QUESTION:
Area and volume Consider the function \(f(x)=\left(9+x^{2}\right)^{-1 / 2}\) and the region R on the interval [0,4] (see figure).
(a) Find the area of R.
(b) Find the volume of the solid generated when R is revolved about the x-axis.
(c) Find the volume of the solid generated when R is revolved about the y-axis.
ANSWER:
SOLUTION 59E
STEP 1
Given the function
(a).we have to find the area of R.
The area between the graph y=f(x) and the x-axis is given by the definite integral.
Since