Explanation Given: Formula used: Calculation: x = cos θ , z = − sin θ , y = 0 Therefore, d x = − sin θ d θ , d y = 0 , d z = − cos θ d θ ∫ y 2 d x + z 2 d y + ( 1 − x 2 ) d z = ∫ 0 π / 2 ( 1 − cos 2 θ ) ( − cos θ ) d θ = − ∫ 0 π / 2 cos θ d θ + ∫ 0 π / 2 cos 3 θ d θ

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 17.2, Problem 32E

To determine

To evaluate: The line integral $\int y^{2} d x + z^{2} d y + (1 - x^{2}) d z$ along the quarter of the circle of radius 1 in the xz plane with center at the origin in the quadrant $x \geq 0, z \leq 0$ .

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Chapter 17.2, Problem 31E

Chapter 17.2, Problem 33E

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Chapter 17 Solutions

Calculus - Standalone book

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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The line integral ∫ y 2 d x + z 2 d y + ( 1 − x 2 ) d z along the quarter of the circle of radius 1 in the xz plane with center at the origin in the quadrant x ≥ 0 , z ≤ 0 .

Solution Summary: The author evaluates the line integral y, d x + z, along the quarter of the circle of radius 1, with center at the origin in the quadrant

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To evaluate: The line integral $\int y^{2} d x + z^{2} d y + (1 - x^{2}) d z$ along the quarter of the circle of radius 1 in the xz plane with center at the origin in the quadrant $x \geq 0, z \leq 0$ .

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Chapter 17 Solutions

The line integral ∫ y 2 d x + z 2 d y + ( 1 − x 2 ) d z along the quarter of the circle of radius 1 in the xz plane with center at the origin in the quadrant x ≥ 0 , z ≤ 0 .

Solution Summary: The author evaluates the line integral y, d x + z, along the quarter of the circle of radius 1, with center at the origin in the quadrant

Videos

To evaluate: The line integral ∫y2dx+z2dy+(1−x2)dz along the quarter of the circle of radius 1 in the xz plane with center at the origin in the quadrant x≥0,z≤0.

Want to see the full answer?

Chapter 17 Solutions

To evaluate: The line integral $\int y^{2} d x + z^{2} d y + (1 - x^{2}) d z$ along the quarter of the circle of radius 1 in the xz plane with center at the origin in the quadrant $x \geq 0, z \leq 0$ .