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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.

60. x = t2t3, 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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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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