   Chapter 10.3, Problem 69E

Chapter
Section
Textbook Problem

Surface Area In Exercises 69-72, write an integral that represents the area of the surface generated by revolving the curve about the x-axis. Use a graphing utility to approximate the integral.Parametric Equations Interval x = t 3 , y = t + 2 0 ≤ t ≤ 2

To determine

To calculate: The integral which represents the area of the surface generated by revolving the curve about the x-axis. Also, approximate the integral of the parametric equations, x=t3 and y=t+2 over the interval [0,2] by the use of graphing utility.

Explanation

Given:

The parametric equations, x=t3 and y=t+2, and the interval of t is [0,2].

Formula used:

If a smooth curve C is given by x=f(t) and y=g(t) such that C does not intersect itself on the interval atb, except possibly at the endpoints, then the area S of the surface of revolution formed by revolving C about the x-axis is given by the following.

s=2πabg(t)(dxdt)2+(dydt)2dt

Calculation:

Consider the parametric equations, x=t3 and y=t+2

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