This exercise is adapted from a problem from the textbook. Consider the line integral [(x - y) dx + (x + y) dy where is the curve going counterclockwise around the triangle with vertices (0,0), (1,0), and (0, 1). (a) Sketch a graph of the triangle described above. triangle. Indicate the direction of the curve on the (b) Find parameterizations of the three line segments forming the edges of the triangle. Note: This works the same way that it did in 3D with t, except with two components each instead of three. Review Section 12.5 for details. (c) Evaluate the integral above by first expressing the line integral as a single-variable in terms of the parameter t.

This exercise is adapted from a problem from the textbook. Consider the line integral [(x - y) dx + (x + y) dy where is the curve going counterclockwise around the triangle with vertices (0,0), (1,0), and (0, 1). (a) Sketch a graph of the triangle described above. triangle. Indicate the direction of the curve on the (b) Find parameterizations of the three line segments forming the edges of the triangle. Note: This works the same way that it did in 3D with t, except with two components each instead of three. Review Section 12.5 for details. (c) Evaluate the integral above by first expressing the line integral as a single-variable in terms of the parameter t.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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