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Math
CalculusMultivariable Calculus8th Edition

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Chapter 10.2, Problem 60E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
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Problem 2E
Problem 3E
Problem 4E
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Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis. Then use your calculator to find the surface area correct to four decimal places.

60. x = t2 − t3, y = t + t4, 0 ≤ t ≤ 1

To determine

To find: The surface area of the curve for the parametric equation x=t2−t3 and y=t+t4.

Explanation

Given:

The parametric equation for the variable x is x=t2−t3.

The parametric equation for the variable y is y=t+t4.

The value t ranges from 0 to 1.

Calculation:

The surface area of the surface obtained by rotating curve about the x axis S=∫012πy(dxdt)2+(dydt)2dt.

The value t ranges from 0 to 1.

Differentiate the variable x with respect to t.

x=t2−t3dxdt=3t−3t2

Differentiate the variable y with respect to t:

y=t−t4dxdt=1−4t3

Write the surface area formula.

S=∫132πy(dxdt)2+(dydt)2dt

Substitute (3t−3t2) for dxdt and (1−4t3) for dydt in the above equation

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