Evaluate (25 + 2xy – 2y²) ds, where C is the part of the circle x² + y² = 25 in the first quadrant. Select one: O a. 25 О . 125 Ос. 4т + 2 O d. 2n +1 O e. o

Q: J, Te-4): dz where I is a circle z – 2 =5. Find -32 Ti 96 Ti - 96 Ti 32πί

A: In the given question we have to find the integration…

Q: -dz, C: counterclockwise circle Jz- i|=3. +1 2. Determine

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Q: Evaluate xy? ds where Cis the first quadrant of the circle, x² + y²= 16 . .A 256 3 .B 8192 5 .C 8192…

A: By line integration formula problem is solved

Q: Which equation represents a circle with center (-4, 9) and radius 7? 1.(x+4)^2 + (y-9)^2 = 7…

A: Use the standard form of equation of circle when centre and radius are given.

Q: 4. Evaluate y ds where C is the upper half of circle x? + y? = 9, traversed in the counterclockwise…

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Q: b) Use Greens theorem to findf x² ydx – xy?dy where C is the circle x? + y? = 4 going counter clock…

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Q: Evaluate . (x² +y) dS where C is given as the part of the circle x? + y² = 9 between the points %3D…

A: given integral ∫Cx2+ydS where C is given as the part of the circle x2+y2=9 between the points 3,0…

Q: 4- Find the center and radius of the circle: x² + y? + 4x – 6y – 3 = 0

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Q: A. Determine the center and radius of the following circles. 1. x2 + y2 – 8x + 2y + 13 = 0 2. х2 +…

A: As per the company guidelines we can solve first three parts  . I hope that the given solution will…

Q: Evaluate | xy2 ds where C is the first quadrant of the circle, x2 + y2= 16 . .A 8192

A: We need to evaluate ∫cxy2ds Where c is the first quadrant of circle x2+y2=16

Q: If F = V(2x? + 4y*), find fGF . di where C is the quarter of the circle a? + y? = 4 in the first…

A: Solution :-

Q: (b): §. (x* – 2y³)dx + (2x³ – y*) dy, where C is the circle x² + y² = 4.

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Q: Find the center and radius of the circle defined by the equation given below. x2 + 2x + y? + 10y =…

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Q: In the diagram, QR = ST = 80, CU = 5x, and CV = 7x - 12. Find the radius of Circle C. %3D %3D %3D W…

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Q: x + y? – 14x + 6y + 54 = 0 is the equation of a circle with center (h, k) and radius r for: %3D h =…

A: Lets find radius r  and  center(h,k).

Q: 3 8. Determine the centre and the radius of the circle x² + y² – 5x + 12y – 6.75 = 0. State your…

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Q: Find the distance between the centers of the two circles x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x…

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Q: What are the radius and center of the following circle? x2 + y? + 4x – 4y + 4 = 0

A: Solution: The objective is to find the centre and the radius of the given circle

Q: Evaluate / (x? – 2y) dx + (2x – y²) dy where C is the circle x? + y = 4.

A: To solve the given integral problem.

Q: follows N2. 6. Find the center and radius of the circle described by the equation r +y + 6x – 4y –…

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Q: (b) Im(2)dz, where C is the circle |z| = 2 traversed once counterclockwise.

A: i have used the parametrization of circle  |z|=2 , z=2e^it where 0<= t <=2pi and the…

Q: e2z dz, I (z+ 1)* (b) Where C is a circle |z| = 3

A: The given integration is ∮ce2zz+14dz where c is the circle z=3 Here the pole z=-1,which is of order…

Q: Evaluate (r2 + y?)ds, C is the left half of the circle with radius 4 centered at (0,0) and is…

A: We calculate this by using concepts of line Integrals !

Q: Let f (2) = 5. Let C be the circle |z| = 2 in the counter-clockwise direction. What is 2ni Tf(2) dz?

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Q: Evaluate . (x-y)dS where C is given as the part of the circle x2 + y? = 4 between the points %3D…

A: Use parameterization to solve given problem. x = 2 cos t y = 2 sin t.

Q: Q2 Sf(2)d2, where Sfrzidz, f(2) =(2+2) and c is Evaluate the circle 2=2e

A: C traversed  counter clockwise. If clock wise then value will be negative.

Q: D. Reduce to standard form and draw the circle whose equation is 4x^2 + 4y^2– 4x – 8y – 31 = 0.

A: topic - equation of circle in standard form graph of circle can be drawn by taking (0.5 ,1 ) as…

Q: in the figure below, Z is the center of the circle. Suppose that QR=4x-5, ST=7,ZU=8, and ZV=8. Find…

A: Solution

Q: 35. Find the length of XZ in the circle. Y is the center point. YZ = 3, and m2XYZ-60 A. 3 7 B. C. 6…

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Q: 2² + y? 14x + 10y + 10 = 0 is the equation of a circle with center (h, k) and radius r for:

A: Given : x2+y2-14x+10y+10 = 0

Q: What are the radius and center of the following circle? x² + y2 + 4x – 4y + 4 = 0

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Q: C. Determine the center and radius of each of the following circle. 9. x + y - 10x + 12y + 41 = 0…

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Q: Which equation represents a circle with center (1, -3) and radius of 16 units? O (x+1)2 + (y-3)2 =…

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Q: Evaluate | ry ds where C is the right half of the circle r + y = 9 %3D

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Q: Evaluate xy? ds where C is the right half of the C circle x? + y? 4

A: C is the right half of the circle: x2+y2=4. Therefore use the parametrisation: x=2 cos t y=2sin…

Q: If F = V(2x2 + 4y), find F dr where C is the quarter of the circle x2 + y? = 1 in the first…

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Q: 3. Rewrite the following equation for a circle in standard form, identify center and radius. x² +y?…

A: The algebraic identities are a±b2=a2+b2±2ab, where a, b are any algebraic expression. Rearrange the…

Q: Identify the following parts of a circle. 1. Point A В 2. AB 3. FD 4. AG 5. BD 6. BF 7. BDG 8. BFD…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: In the diagram, O is the center of a circle with OU= OV, and %3D XY= 13 cm. 国 Y

A: YZ=13 Because XY and YZ at the same distance from circle's center.

Q: ㅠ Use Green's theorem to find: where C is the circle x² + y² = 4 going counter-clockwise. -8T […

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Q: 1. C is the center of the circle. Calculate x. C 57° 57°

A: Here, C be center of the circle. We need to find the value of x.

Q: A. Determine the center and radius of the following circles. 1. (x - 4)2 + y + 8)? = 100 2. (x + 1)²…

A: I have answered first three subparts as per the guidelines.

Q: answer by shading the circle corresponding to your choice. y = ce-2t + 3t2 o y' + 6y = 2t(t + 1) o…

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Q: Find the center and the radius of each circle. 36 17. (x + 3) + y 18. (x + 7) + (y – 8)² = 20. (x +…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the points on the circle x^2+y^2=45 that are closest to and farthest from (1,2)

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Q: Determine the center and radius of the following circle equation: x2 + y? – 2x – 12y + 36 = 0 -…

A: The standard form of the circle is given by the equation where is the center and r is the radius of…

Q: ARST is shown. XU = -4y + 20 and XW = 6y + 10. Find the radius of the inscribed circle of ARST…

A: The inscribed circle is the circle inside the triangle touching all three sides of the triangle.…

Q: Find the center and radius of the circle x2 + y2 + 4x = -2y +11. Sketch the circle. %3D ....-

A: Convert the equation of circle into standard form: (x-h)^2 + (y-k)^2 = r^2

Q: Vhat is the equation of a circle with center (3, –7) that goes through the oint (1, 1)? D (x – 3)2 +…

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Q: If F = V(4x² + 4y³), find ſ, F · dř where C is the quarter of the circle x? + y? = 9 in the first…

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Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: