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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
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.

59. x = t + et, y = et, 0 ≤ t ≤ 1

To determine

To find: The surface area of the curve for the parametric equation x=t+et and y=et.

Explanation

Given:

The parametric equation for the variable x is as below.

x=t+et

The parametric equation for the variable y is as below.

y=et

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=t+etdxdt=1et

Differentiate the variable y with respect to t:

y=etdxdt=et

Write the surface formula for the curve.

S=132πy(dxdt)2+(dydt)2dt

Substitute (1et) for dxdt and (et) for dydt in the above equation

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