Chapter 16.4, Problem 19E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use one of the formulas in (5) to find the area under one arch of the cycloid *x* =* t* − sin *t*, *y* = 1 − cos *t*.

To determine

**To find**: The area under one arch of the cycloid.

Explanation

**Given data:**

Parametric equations are

Consider a curve

Differentiate equation (1) with respect to *t*.

Differentiate equation (2) with respect to *t*.

Consider a curve

Differentiate equation (3) with respect to *t*.

Differentiate equation (4) with respect to *t*.

The area of curve *C*, which is one arch of cycloid is the union of regions of curves

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