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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.

58. x = sin t, y = sin 2t, 0 ≤ tπ/2

To determine

To find: The surface area of the curve for the parametric equation x=sint and y=sin2t.

Explanation

Given:

The parametric equation for the variable x is as below.

x=sint.

The parametric equation for the variable y is as below.

y=sin2t.

The value t ranges from 0 to π2.

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 π2.

Differentiate the variable x with respect to t.

x=sintdxdt=cost

Differentiate the variable y with respect to t.

y=sin2tdxdt=2cos2t

Write the length of the curve formula.

S=0π22πy(dxdt)2+(dydt)2dt

Substitute (cost) for dxdt and (2cos2t) 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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