   Chapter 10.2, Problem 60E

Chapter
Section
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=t2t3 and y=t+t4.

Explanation

Given:

The parametric equation for the variable x is x=t2t3.

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=t2t3dxdt=3t3t2

Differentiate the variable y with respect to t:

y=tt4dxdt=14t3

Write the surface area formula.

S=132πy(dxdt)2+(dydt)2dt

Substitute (3t3t2) for dxdt and (14t3) for dydt in the above equation

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