oV5+ 2x² + 2y° dA.Work problem 2 ")You mustprovide clear and detailed solutions foreach of the following questions:Question 1half of the circle x +y = 9. SketchD, and give D in the polar coordinates.Evaluate the following double integral:is] Let D be the leftIL V5 + 2. + 2y? dA.DQuestion 2.] Let E be theregion below xfirst octant. Evaluate the following triple2y + z -1 in the-integral:I tu av.E

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Answered: Work problem 2 " ) You must provide…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Good day, please help me with Question 2.2.2 sub part 1 - getting the polar and cartesian coords for the integral. I just want to compare my answers as no solution was given in class.
Use one of the formulas in (5) to find the area under one arch of the cycloid x = t - sint and y = 1 - cost. Work seen below. How were the parametric equations x = 2pi - t (3) and y = 0 (4) found? This is an explanation of the problem but the work is not 100% clear.
1. Consider the area enclosed between the circle x^2 + y^2 = 4, the line y = 3, y = x, and y = -x. (a) Express these Cartesian equations as polar equations.
2. Consider the polar curves r = 4 - 2cosθ and r = 2 + 2cosθ. In this problem, we want to find the area of A, B, and C pictured below. (c) B is the area inside both r = 2 + 2cosθ and r = 4 - 2cosθ. Find the area of B. (Hint: What happens at the angle where the two polar curves intersect? Your answer should involve a sum of two polar integrals.)
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Find the surface area resulting from the rotation of the parts in the first and fourth quadrants of the polar curve r = 1 - cos(θ) around the line θ=π/2, formulate only the necessary integral without solving it. Please solve a question quickly I need this Answer at half time Quickly. Please
i need to convert below z=64-4*x^2-4*y^2 and above the xy-plane into polar coordinate however i am stuck in determining the region.
The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1, is given by what integral?
1)Basically, what changes when we exchange the Cartesian coordinates for the polar coordinates? 2 – In the case of a double integration, what changes if we change the order of integration? (Ex: instead of doing dy dx, do dx dy)
Find the length of polar curve of r=θ^2 with θ less than or equal to 7π/4 and greater or equal to 0.
True or False. 1. If one uses the horizontal strip/element as a representative area, then the infinitesimal change may exist in either x or y variable depending on the orientation of the curve. 2. If a polar equation r = f (θ) is made θ = f (r), the limits of integration r1 and r2 must be obtained from the corresponding values of θ1, and θ2 which bound the area of concern. 3. The point (-13, -110π/4) is located between 0 and 1.80π region of a polar coordinate system and is identical to (13, 3π/2). 4. For any rose-petal curve in the form r = a cos(nθ) with the same maximum length a, the equation with the greater number of petals m, (m= n for odd, 2n for even) will always yield to larger area of the curve. 5. Any polar equation can be made rectangular. 6. The Theorem of Pappus will always be applicable to determine the volume of solid revolution for as long as the centroid of the figure and its distance from the axis of revolution are given. 7. The shell method is most applicable for…
Hello! I was wondering how we are supposed to get to the boundaries of the angle when replacing x and y with the polar coordinates rcos and rsin... For r I understand that the boundaries will be from 0 to a, since x2+y2<=a2, so r2<=a2, and hence r<=a, but how do we get to the boundaries of the angle needed to evaluate the integral?

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Work problem 2 " ) You must provide clear and detailed solutions for each of the following questions: Question 1[ half of the circle x +y = 9. Sketch D, and give D in the polar coordinates. Evaluate the following double integral: is] Let D be the left 5+2x2 + 2y? dA.