Evaluate the integral | (3x – 2 y + :)ds where C is the curve, C, and C, as shown. 3- y² + z² 2. 3 (3, 1, 0)

Q: Find the line integral of F(x, y) = (x²– y², 2.xy) = (P, Q) along the boundary of the rectangle [0,…

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Q: evaluate the line integral along the curve C. Scv+z) d s, C is the straight-line segment x = 0, y =…

A: To Evaluate∫C(y+z)dswhere C is straight line segmentx=0  ----(i)y=3-t -----(ii)z=t…

Q: Calculate the integral of the line K = (3z + z – 2)dz Where C It's the curve y = x? from x = 0 to x…

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Q: Evaluate the line integral f e-*(cos y dx - sin y dy), where c is the rectangle with vertices (0,0),…

A: The line integral function is ∫Ce-xcosydx-sinydy. The vertices of the rectangle is 0, 0, π, 0, π,…

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: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤t≤ 1. √(x + 3y²) dy…

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Q: Evaluate the line integral, where C is the given curve C is the line segment from from (0, 0, 0) to…

A: Here   , ds = dx dy dx  Now we  will evaluate the integral

Q: Evaluate the line integral along the given paths. | xy ds (a) C: line segment from (0, 0) to (5, 4)…

A: We need to evaluate,                          . For (a), .

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…

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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: 7. Evaluate the line integral by using Green's Theorem feve'dx +2e*dy C is the rectangle with…

A: Green's Theorem, ∫CPdx+Qdy=∬D∂Q∂x-∂P∂ydA Compare ∫CPdx+Qdy=∫Cyexdx+2exdy Implies that, P=yex, Q =…

Q: (2) Find the work done by F(x, y) = (2xy³, 4x²y²) moving a particle on the path C where C is the…

A: Formula: Work done W by a force field F on a particle on the path C is: W=∫C F·dr It is given that…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve.  xy2…

A: Our Aim is to evaluate the line integral along the given positively oriented curve xy2 dx+3x2y dy…

Q: Find the integral of r(t) = (3t2 + 4t, 2, e') from 0 to 1.

A: Consider the following vector: rt=3t2+4ti^+2j^+etk^ Integrate the above vector:…

Q: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: Evaluate the line integral, where C is the given curve.     C xeyz ds, C is the line…

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Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(r) 1 In r %3D where 1<r <…

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Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-2,…

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Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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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 (e*y+ 2x) dx + (e* + 1) dy, where C is a smooth curve from the point (0,…

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Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = xe, OsxS 8 osxs 8 dx

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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: Set up, but do not evaluate, an integral for the length of the curve. y = x - 3 In(x), 1< x < 4 4 dx

A: The given curve y=x-3 ln(x), 1≤x≤4

Q: 1+y dy

A: We can solve the given integral as follows:

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: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. y10 dx + x6…

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Q: dz 10. Evaluate the integral where C is a simple closed curve cz(z - 1)' in the positive direction…

A: The integral ∫Cdzzz-1, where C is the simple closed curve in the positive directionthat contains the…

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, 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 along the path C given by x = 2t, y = 8t, where 0 sts 1.

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Q: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

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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: Evaluate the integral a sin y ds where C is the line segment from (0, 3) to (4,6),

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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. |(x+3y)dx+(x- y)dy, C: x= 2cost, y = 4sint, 0sts 4…

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Q: Find the integral f(r, 0) = 4r², where 1 <r< 3, -T < e <n of

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

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Q: Find the line integral of C in two ways; A) Directly. B) Using Green's theorem. C eata formed by the…

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Q: Set up the iterated (triple) integral for the integral ]]] xy¹z³ dV where S is the tetra- S hedron…

A: We will find limits of variable and then find value of integral

Q: 4. Evaluate the double integral D where D is enclosed by the curves y = a², y = 3x.

A: First we will draw the graph for given curves from that we will find the limits of x,y as shown…

Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

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Q: Use Green's Theorem to evaluate the line integral , 6y² dx + 5x² dy, where Cis the boundary of the…

A: Green's Theorem: ∮C(Pdx+Qdy)=∫∫R∂Q∂x-∂P∂ydA

Q: Evaluate the line integral along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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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: Evaluate the line integral, where C is the given curve. x sin(y) ds, C is the line segment from (0,…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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