Explanation Given information: A curve C is specified by C : part of circle x 2 + y 2 = 9 with x ≤ 0 and y ≥ 0 oriented clockwise A vector valued function F ( x , y ) = 〈 x 2 , x y 〉 Formula used: Suppose that curve C is a parametric curve r ( t ) where a ≤ t ≤ b , then the line integral of ∫ C F ⋅ d r is given by ∫ C F ⋅ d r = ∫ C F ( r ( t ) ) ⋅ r ′ ( t ) d t Calculation: Consider the curve C. Part of circle x 2 + y 2 = 9 with x ≤ 0 and y ≥ 0 oriented clockwise Here, radius of the circle is 3 and portion specified is left side of x − axis and positive side of y -axis. That is the quarter area of 2 nd quadrant only. Let us consider the parametric equation for the portion

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Chapter 16.2, Problem 21E

To determine

To evaluate:

The integral ∫CF⋅dr for the oriented curve specified.

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Chapter 16.2, Problem 20E

Chapter 16.2, Problem 22E

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6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4

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Find a parameterization for a circle of radius 4 with center (-4,-6,-3) in a plane parallel to the yz plane. Write your parameterization so the y component includes a positive cosine.

Chapter 16 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E

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