Chapter 13.3, Problem 12E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4*x*^{2} + *y*^{2} = 4 and the plane *x* + *y* + *z* = 2.

To determine

**To find:** The length of *C* of the cylinder

Explanation

**Given data:**

Consider *C* is curve of intersection of cylinder

The expression for cylinder is,

Divide by 4 on both sides of equation (1).

The projection of the curve *C* onto the *xy*-plane is an ellipse

Consider the parameter following parameters.

Since *C* is also lies on the plane, the expression for the plane is,

Re-arrange equation (3).

Substitute
*x* and
*y* in equation (4),

The vector equation

Substitute
*x*,
*y*, and
*z*,

Differentiate the equation with respect to *t*.

Take magnitude on both sides

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