Verify the Fundamental Theorem for line integrals for the case that C is the top half of the circle x^2+y^2-1 traversed in the counter clockwise direction and f(1, y) = ry + I Note: In order to solve you need to do the following: a) evaluate f(B) - f(A); b) evaluate the line integral (FTLI) as requested; c) verify that the answers in parts a) and b) are equal. 1.6

Q: (a) Express the mass M of a thin wire in 3-space as a line integral. (b) Express the length of a…

A: a) The objective is to express the mass M of a thin wire in 3-space as a line integral. The mass of…

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. ye* dx…

A:

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

A:

Q: Use the Fundamental Theorem of Line Integrals to calculate E. dr exactly. F = 6 sin(6x + y)i +…

A: Given

Q: 50.) Show how to use a line integral to find the area of a circular disk of radius r

A:

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

A: .

Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

A:

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

A:

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. O x2y dx,…

A:

Q: Find the moment of inertia about the​ x-axis of a thin plate bounded by the parabola x=2y-3y2 and…

A: Given that the equation of the parabola,x = 2y – 3y2and the equation of linex + 7y = 0

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: Use Green's theorem to determine the value of the integral where the curve x2 + 4 = 1 traveled…

A:

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 -

A:

Q: Why does in some cases, the arc length is changed to its parametric form to determine the line…

A:

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

A: Formulae used, d(ex)dx=ex d(x)dx=1and         ∫abexdx=exab

Q: Evaluate the integral xyzdV where E lies between the spheres with radius 2 and 4 and above the cone…

A: Using spherical coordinates,

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

A:

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

A:

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

A:

Q: y' = 2 – 3xy; {-1<x<4, -4 < y s 4}

A: To plot direction field we plot small lines with slope calculated form differential equation after…

Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: iii) Set up an integral for the area of the surface generated by rotating the curve about the…

A:

Q: Evaluate the line integral (direct method) |(3x– y) dx – x dy , where C consist of the parabola y=…

A: Given integral is, ∫C(3x-y)dx-xdy

Q: The amount of work that a force field does on a particle as it moves along the boundary of a…

A:

Q: y*dx + x*dy = (N, – M,) • dA (м, - м,) ал

A:

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

A: line integral

Q: Is the integral A.dr path independant if A=(2x-y)i+(x+y)j? Evaluate closed line integral around a…

A: Given line integral is, ∮A.dr=∮[(2x-y)i+(x+y)j] dr  The condition for the path independence of a…

Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: Work done= Force * distance                     =(force due to Weight)* distance

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

A:

Q: 4) Write the integral to calculate the outward flux through F = (-yx2, xy,-z) across the sphere with…

A:

Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x - y)dy Ic

A: Put the value of x and y and then simple integration.

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. L(y -…

A:

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

A:

Q: image attached

A:

Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

A:

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

A:

Q: Find a center of mass of a thin plate of density δ=1 bounded by the lines y=x and x=0 and the…

A: Given that density is 1 and thin plate is bounded by the lines y = x, x = 0 and y = 30 – x2

Q: Determine whether the Fundamental Theorem of Line Integrals (FTLI) can be used to evaluate…

A:

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

A:

Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: set up the integral for w9rk requireded to pump the water in the drum shaped solid to the goal line

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

A: Using the Green's theorem.         ∫C  (M dx+N dy)=∫∫D ∂N∂x-∂M∂ydA.    ∴    ∫C y…

Q: Let F = 4(x + y) i + 8 sin(y) j. Find the line integral of F around the perimeter of the rectangle…

A:

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

A: Given the line integral

Q: Is the integral / A · dr path independent if A = (2x - y)i+ (x + y)j? of Evaluate A · dr around a…

A:

Q: Evaluate 6z ds where Cis the curve y = -72² from (-1,-7) to (1, -7). Enter the scalar line integral…

A: To evaluate ∫C6xds where C is the curve y=−7x2 from −1,−7 to 1,−7.

Q: Evaluate the following line integrals. Do not resort to parametrization, but instead use an…

A:

Q: . The work required to move a mass m "infinitely far" from a planet of radius R and mass M is given…

A:

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)