For the vector field G = (yety + 4 cos(4x + y))i + (xey + cos(4x + y)) 5 I find the line integral of G along the curve C from the origin along the x-axis to the point (4,0) and then counterclockwise around the circumference of the circle x² + y² = 16 to the point (4/√√2,4/√2). So G. dr =

Q: For the vector field G = (yey + 3 cos (3x + y))i + (xeªy + cos(3x + y)), find the line integral of G…

A: We find the required integrtion using fundamental theorem of line Integral.

Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: x-y, z + y + 3,z²) and the net is decribed by the equation y = 1- x² - z on

A:

Q: Calculate grad div F+ curl F at P(-1, 1, 1) where − = (3xz²)i + (xy)j + (2yz)k. O 7i+ 4j - 3k D-3i -…

A: we will find the required.

Q: Sketch the vector field F(x, y) = xj, the line segment from (1, 3) to (9, 3), and the line segment…

A:

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: Since the surface is whole sphere, that is S is closed so we can apply Gauss Divergence Theorem.

Q: Consider the vector field v(x)=(y/(x^2+y^2))i − (x/(x^2+y^2)) j + 4k. Calculate ∫Cv dr, where C is…

A:

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: Evaluate the line integral of the vector field (3x2 + 3y + 2xy, 3y2 + 3x + x2) along the curve y = x…

A:

Q: 3. Let F = (x - y, xy) and C be arc of the circle x? + y? = 4 traversed counter-clockwise from (2,0)…

A:

Q: 1-2 Find the domain of the vector function. 1. r(t) = (10(1 In(t + 1), t - 2:21

A:

Q: For the vector field (x2,0₁ - 2x² -z²), evaluate its line integral along the closed curve, made by…

A:

Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

A:

Q: To calculate from elliptic curves we will use a simple approximation. For example, consider the…

A: Consider, the curve is y² = x3 + 17. The points are given by P=-1,4 and Q=2,5.

Q: Find the parametrization of two different curves from the point (2,4) to (3,9). Compute the work…

A: Given point (2,4)  and (3,9)now equationof line passing through two point is given by…

Q: Let F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

A:

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: We have to find the heat flow out of the sphere of radius

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: A sphere of radius 1 is x2 + y2 + z2 = 1. Parametrize the sphere as follows:Now,calculate the…

Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

Q: Show that the vector field F(x, y, z) = (-ycos(8x), 8x sin(-y), 0) is not a gradient vector field by…

A:

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: A sphere of radius 1 is x2 + y2 + z2 = 1. Parametrize the sphere as follows:Now,Now,calculate the…

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A:

Q: 5) Find the flux of F = (-2y, -x) on the circle of radius 2 centered at the origin. Use the vector…

A: When the field vectors are going the same direction as the vectors normal to the surface, the flux…

Q: F(x,y) = (4xy. – 3y²) (A Vxi = -4x B) V XF - - 2y C vxF V xF - - 2y + 8x D VxF - 4x - 6y

A: solution