Area and volume Consider the function f(x) = (9 + x2)–1/2

Chapter 4, Problem 59E

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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.

                                               

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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

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