Evaluate F dr for the curve. Discuss the orientation of the curve and its effect on the value of the integral. F(x, y) = 3x2i + 4xyj (a) r1(t) = 2ti + (t 1)j, 1 s ts 3 10 (b) r2(t) = 2(3 – t)i + (2– t)j, osts 2

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

A: In the above line integral there are two segments which needto be seperated. First (0,0) to (1,0) so…

Q: 3. Evaluate the three integrals f dz J, dr. f dy, and where f(x, y, z) = x – y + z and C is the…

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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, where C is the given curve. | (x/y) ds, C: x = t3, y = t4, 1sts 2

A: Given: I=∫C(xy)dsC: x=t3  and  y=t40≤t≤2

Q: 22. Find the line integral of f(x, y) = x – y + 3 along the curve r(t) = (cos t)i + (sin t)j, 0 < t…

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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: Calculate the integral of f(x, y, z) = 3x² + 3y² + zª over the curve c(t) = (cos t, sin t, t) for 0…

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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 by the two following methods. pxy dx + x?y³ dy C is counterclockwise…

A: Sketch the graph of the triangle with vertices points (0, 0), (1, 0), and (1, 4) as shown below:…

Q: Calculate the integral (x – y) dx + (x + y) dy I = x2 + y2 where L is along the curve y = cos x,…

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Q: Evaluate the line integral by the two following methods. "line integral"xy dx + x2 dy C is…

A: Given line integral i∮ xy dx + x2dy C is counterclockwise around the rectangle with vertices (0,…

Q: Evaluate the line integral by two methods: (a) directly and (b) using Green’s Theorem.3. ∮C xy dx +…

A: According to Greens theorem :

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: Evaluate the line integral for the given curve C. S-ds, C: r(t)= (t',t*),1<t<2 cy ||

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Q: Set up, but do not evaluate, an integral for the length of the curve. x = y + y, 4sys6 222 L V1+ (1…

A: topic - length of the curve calculator

Q: Find the line integral of ƒ(x, y) = x - y + 3 along the curver(t) = (cos t)i + (sin t)j, 0 &lt;_ t…

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Q: B) Evaluate the line integral of the function P(x,y) dx + Q(x,y) dy. over the curve C where…

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Q: Calculate the integral of f(x,y,z)=3x2 +3y2 +z4 over the curve c(t)=(cost,sint,t) for 0≤t≤π. ∫c…

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

A: To evaluate the line integral, consider the curveC1 consisting of the line segment from0,0to9,1. The…

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

A:

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: 17. Along the curve r(t) = ti – j+ t²k, 0 < t < 1, evaluate each of the following integrals. a. r +…

A: (a).           If the equation of curve x = x(t), y = y(t) , z = z(t)         Then the line integral…

Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r ±1 and…

A: According to cauchy’s integral formula for any region C,

Q: 21. Find the line integral of f(x, y) = ye along the curve r(t) = 4ti – 3tj, –1 < t < 2.

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = xe, O sxs 2 dx

A: The equation of the curve and the interval is given by y = xex6 ; 0≤x≤2 To set-up : An integral for…

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: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

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Q: Calculate the integral of C being the curve given below. y= 3+x y= 3-x 6x dS C

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Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: Evaluate the line integral along the given path. (x² + y² + z?) ds C: r(t) = sin(t)i + cos(t)j + 5k…

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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: Find the line integral of ƒ(x, y) = x - y + 3 along the curve r(t) = (cos t)i + (sin t)j, 0&lt;=…

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Q: Find the line integral of f(x,y) = y e* along the curve r(t) = - 5t i – 12t j, - 1sts0. The integral…

A: Use parametric to integration

Q: Evaluate the line integral of f(x,y) along the curve C. 7) f(x, y) = x5 √1+ 4y ,C: y=x², 0≤x≤ 3

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Q: Evaluate the line integral, where C is the given curve. |(2y3 - Vx)dy, c is the arc of the curve y =…

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Q: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

A: We will use greens theorem

Q: Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. C is the…

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Q: (1,0) (1,0) | (x2 – y²) dx – 2x y dy + i | 2x y dx + (x² – y²) dy (0,1) (0,1) Calculate the above…

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

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Q: Evaluate the line integral along the curve C. y² ds, C is the curve r(t) = | 9 sin x + z2 i+ + 5tk,…

A: To find the line integral along with curve C, use the formula,…

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

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Q: 17. Along the curve r(t) = ti – j + t²k, 0 <1< 1, evaluate each of the following integrals. a. (х +…

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Q: Q#03(a): Use Green's theorem to evaluate the line integral f. (x – 3y) dx (4x + y) dy, where C is…

A: Green's theorem

Q: Evaluate the line integral, where C is the given curve ʃc (x+9y)dx +x2dy, where C consists of line…

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = xe, 0 sx s1 1 dx

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Q: Evaluate the integral / | Vf. dr Vf•dr where f (x,y)=xy² and C is a curve from (1, 1) to (2, 3).

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.