Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 7y dx – 7x dy Cis the circle x2 + y² = 4

Q: Set up, but do not evaluate, an integral for the length of the curve. y = 6 cos x, Osxs 27 dx

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Q: Evaluate the line integral Ĥ. dř where Ĥ = e" î + [xe" + In(2)] ĵ + º Â and the curve C is defined…

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Q: Use Green's Theorem to evaluate the line integral below. | (2 - v?) dx + 5xy dy C: r = 1 + cos(0), o…

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Q: Evaluate the line integral , F dr where F (3 sin x, -5 cos y, xz) and C is the path given by r(t) =…

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Q: Use Green's Theorem to evaluate the line integral f(e*c - 2y)dx+(5x+ev* dy, where C is the 15. 2cos:…

A: We need to find integral.

Q: Compute the line integral f 2xy dx + x2 dy along the following curves. (a) C1 along the circle x2 +…

A: A detailed solution is given in steps 2 and 3.

Q: Evaluate the line integral along the curve C. (xz+2) ds, C is the curve r(t) = (-6-2t) i + tj- 2tk,…

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Q: Evaluate the line integral along the curve C. 3xy ds; C is the quarter circle r(t) = (cos t, sin t)…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

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Q: Evaluate the line integral along the curve C. (xz + y) ds, C is the curve r(t) = (-4 - t) i + 2t j -…

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Q: Use Green's Theorem to evaluate the line integral along the given positive (* 2x²y?) dy -4x хе dx +…

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Q: E Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [ 4³…

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Q: Evaluate the line integral, where C is the given curve. | 22 dx + x2 dy + y² dz, C is the line…

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Q: Evaluate the line integral, where C is the given curve. (z? +2xy)dx+ x²dy +2xzdz, where C is the…

A: The b option is true.

Q: Evaluate the line integral along the given path. C: r(t) = sin(t)i + cos(t)j + 3k osts 8

A: The given line integral is ∫Cx2+y2+z2 ds where c is a curve rt=sinti+costj+3k  and  0≤t≤π8.…

Q: Evaluate the line integral by the two following methods. y) dx + (x + y) dy C is counterclockwise…

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Q: Use Green's Theorem to evaluate the line integral Around the Outer circle x2 + y? = 4 & y > 0 as…

A: Given F=ρsinφaρ+ρ2aφ

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xe-4*…

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Q: Evaluate the line integral, where C is the given curve. xy ds, C is the right half of the circle x2…

A: C is the right half of the circle x2+y2=16 thus the parameterization of the circle is x=4cos t and…

Q: Set up, but do not evaluate, an integral for the length of the curve. y - xe, osxs2 dx

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Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).

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Q: Evaluate the line integral, where C is the given curve. Sc (x + 9y)dx + x² dy, C consists of line…

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Q: Evaluate the line integral, where C is the given curve. (x + 5y) dx + x2 dy y (5, 1) (6, 0)

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Q: 2. Evaluate fy³ dx-r³ dy, where C is the circle of radius 2 centered at the origin, in the following…

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Q: Consider the following line integral. xy dx + xy3 dy, C is counterclockwise around the triangle with…

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Q: Evaluate the following line integral along the curve C. - y)ds; C is the line segment r(t) = (t, 3t…

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Q: Given that C is the curve r(t) = (cos t, t), for /2 sts T, convert the line integral | ds to an…

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Q: 1+y dy

A: We can solve the given integral as follows:

Q: Evaluate the line integral along the given paths. y?) ds + (a) C: line segment from (0, 0) to (8,…

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Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (fg) = (7x2,8y?) and…

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Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f,9) = (7x?,8y) and…

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Q: Use Green's Theorem to evaluate the line integral of F = (x°, 6x) around the boundary of the…

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Q: Evaluate the line integral ∫Cxdy−ydx along the curve C defined by the equation y=x3 from the origin…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y? dz, C is the line segment…

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Q: Evaluate the line integral by the two following methods. (x - y) dx + (x + y) dy C is…

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Q: Evaluate the line integral along the curve C. ds, C is the curve r(t) = (-1 - t) i - j+(-1 - t) k,…

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Q: Evaluate the line integral Sp(xi+ yyj) · dr where D is the oriented curve shown below. (1,1) y = x²…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y² dz, C is the line segment…

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Q: Evaluate the line integral by the two following methods. f (x - y) dx + (x + y) dy C is…

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Q: Use Green's theorem to evaluate the line integral for the curve C given in the figure. [8y dx + 7x…

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Q: Evaluate the line integral , F. dr where F = (3 sin x, -5 cos y, xz) and C is the path given by r(t)…

A: To determine the value of the integral.

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. -5x хе…

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Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f.g) = (7x²,8y?)…

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Q: Evaluate the line integral, where C is the given curve. dy, C is the arc of the curve y = Vx from…

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Q: Use the Fundamental Theorem of Line Integrals to calculate /Fd7 where F - 19" 7 + 5y 7 and Cis the…

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…

Q: Evaluate the line integral along the curve C. x² +y² ds, C is the curve r(t) = (2 sin 6t)i + (2 cos…

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Q: Evaluate the line integral along the curve C. (3x² + y²) dx + 2xydy, C: x = cos f, y = sin 1, 0≤1≤ 2…

A: Given integral is ∫C3x2+y2dx+2xydy , where curve C:x=cos(t), y=sin(t), 0≤t≤π2 We need to find the…

Q: Set up, but do not evaluate, an integral for the length of the curve. x = 5 sin(y), osys 2 dy

A: Recall: Length of the curve ,L = ∫ab 1+f'(y)2 dy

Q: Evaluate the integral: L x2 + y² dy dx by using polar coordinates.

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Q: Evaluate the line integral, where C is the given curve. C is the arc the curve y = Vx from (4, 2) to…

A: We have to find the line integral of ∫Cx2y3-xdy, C is the arc of the curve y=x from (4,2) to (9,3)

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: