Sc F. dr where F(x.y) = (3x² – 4v)i + (27 + cos(,³))j

Q: Evaluate the line integral -ydx + xdy along the curve C: y? = Зх from (3,3) to (0,0). NOTE: Enter…

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Q: The line y = 2x and the parabola y = 16x intersect at x= 4. Find by a double integral, the area…

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Q: Assuming that the line integrals in the options are over the unit circle centered at the origin (x2…

A: .

Q: (a) Set up an integral for the length of the arc of the hyperbola xy = 1 from the point (1,1)  to…

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Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

A: The given line integral is ∫c-ydx+xdy along the curve c: y2=6x from (6,6) to (0,0)

Q: Let R be the shaded region bounded by the parabola y = 4 - x², and the lines y = 1- 2x and y= -1, as…

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Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and…

A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

Q: of radius 2, centered at the origin and oriented counterclockwise, and where C2 is the curve…

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Q: Evaluate the line integral -ydx + xdy along the curve C: = = 21x from (21, 21) to (0,0). %3D NOTE:…

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Q: Find the area of the surface generated by revolving the curve on the indicated interval about the…

A: answer is mentioned below

Q: Find the area of the part of the eircle r-4 sin that lies within the sector 0 50s 87 -2/3 3 + V3 3.…

A: It is given that,r=4sinθ, that lies within the sector 0≤θ≤π3we have to find the area of the part of…

Q: Use Green's theorem in order to compute the line integral £ (x – 3)³ dy – y³ dx where is the circle…

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Q: a. Set up an integral for the area of the surface generated by revolving the curve y = tan (x), 5…

A: Consider the given: y=tanxLimits π5≤x≤π4y=tanxdydx=sec2x

Q: Plot a direction field and some integral curves for xy' - 2y = -1 (A) on the rectangular region {-1…

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Q: Evaluate the line integral -ydx+ xdy along the curve C :y = 12x from (12, 12) to (0,0). NOTE: Enter…

A: In this question , we can find the given line integral.

Q: Evaluate the line integral, where C is the given curve. xevz ds, C is the line segment from (0, 0,…

A: We have to evaluate the integral ∫Cxeyzds, where C is the line segment from 0,0,0 and 3,2,4. The…

Q: О 3D 2х — у, 1<x<2 -

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Q: Integrate f(z) = 6 tan(z²) counterclockwise around the unit circle, using Cauchy's integral theorem…

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Q: 6. Set up integrals to compute the arc lengths of the curves y = r², y = 26, y = x¹⁰ defined for z…

A: Let's find arc length of given curves on interval [0,1].

Q: Calculate the integral over a closed path C as given below using Green's theorem. • y?dx + 3xydy The…

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Q: Evaluate the line integral - -ydx + xdy along the curve C : y? = 3x from (3, 3) to (0,0). NOTE:…

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Q: Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of…

A: To evaluate the below line integral. ∫c8y2dx+z2dy+100−x2dz Here c is the quarter of a circle of…

Q: =) Sketch the curve y-x. b) Use the following formulas to set up two integrals for the arc length…

A: for the graph, the second option is correct

Q: Write an integral for the area of the surface generated by revolvingthe curve y = cos x, -π/2 ≤ x…

A: Given data: The equation of a curve is: y=cosx. The limit of x is: .   The expression for the…

Q: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

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Q: 3) . (3x2 — Зуz+ 2xz)dx + (3у? - 3xz + z?)dy + (372 — Зху + х? + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. Find a vector parametric equation for the parabola y = x²…

A: The solution is following.

Q: Evaluate the line integral (2 - u) dz + (3 + æ) dy] where C is the parabolic arc = a² from (0, 0) to…

A: We have to evaluate the line integral.

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

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Q: 2/ Find the line integrals of the ellipse+3= ellipse by x = acos(t) ,y= bsin(t) 1 , parameterize the…

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Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

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Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

Q: Evaluate the line integral Jxy + z)ds where c the arc of circle x + y = 4, z= 0 from (2, 0, 0) to…

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Q: Evaluate the line integral -ydx + dy along the curve C: y = 30x from (30, 30) to (0,0). %3D NOTE:…

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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: Set up an integral that gives the length of the curve y2 + y = 2x from the point (1,1) to (3,2)

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Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: Find the area of the surface obtained by rotating y = cosh x over [−ln 2, ln 2] around the x-axis.

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Q: Evaluate the line integral (y + z) ds along the curve C defined by the straight-line segment æ = 0,…

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Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

A: given curve y=2x over the interval [4,9]

Q: 7) Find the area of the surface that is formed by revolving the function y = 2 x on the interval %3D…

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Q: 8K Use Green theorem to eva luate the . line integral : 3. 3 where c is ニ thecircle

A: Given the line integral

Q: The area of the region enclosed by a nonnegative polar curve r = f(0) (a <o< B) and the lines 0 = a…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y = 3x from (3, 3) to (0,0). NOTE: Enter…

A: We have to find the line integral ∫C-ydx+xdy along the curve C: y2=3x from (3,3) to (0,0)