   Chapter 8.2, Problem 5E

Chapter
Section
Textbook Problem

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x-axis and (ii) the y-axis. (b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places. 5. x = y + y3, 0 ≤ y ≤ 1

(a) (i)

To determine

To set up: An integral for the area of the surface obtained by rotating the curve about x-axis.

Explanation

Given information:

The equation of the curve is x=y+y3,0y1 .

Calculation:

Show the equation of the curve.

x=y+y3 (1)

Calculate the area of the surface obtained by rotating the curve about x-axis:

S=cd2πy1+(dxdy)2dy (2)

Here, S is the area of the surface obtained by rotating the curve about x-axis and cyd .

Differentiate both sides of Equation (1) with respect to y

(ii)

To determine

To set up: An integral for the area of the surface obtained by rotating the curve about y-axis.

(b) (i)

To determine

To evaluate: the surface area of the curve about x-axis by using numerical integration capability of the calculator.

(ii)

To determine

To evaluate: the surface area of the curve about y-axis by using numerical integration capability of the calculator.

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