   Chapter 10.2, Problem 58E

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.58. x = sin t, y = sin 2t, 0 ≤ t ≤ π/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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