2. Compute the line integral of f(r, y) = r over the curve C, where C is a triangle formed by joining the points (0,0), (1,0), (0, 1), in that order.

Q: Compute the line integral 는 (J Where c is the part of Aheecrele xh ayt=g in the first quadrent from…

A: We will evaluate the given line integral.

Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

A:

Q: Compute the line integral of the scalar function f(z,y, 2) = 2z² + 8z over the curve c(t) = (e*, t²,…

A:

Q: Find the line integral of f (x, y,z) = -x + y + z over the straight-line segment from (1, 2, 3) to…

A:

Q: Evaluate the line integral along the given path: 1. So ry ds, where C : r(t) = 4ti + 3t²j, 0 < t <…

A:

Q: 2. Evaluate the given line integral, | (-y,x – y) · dR, where C is the line segment from (1,0) to…

A: To find the line integral we use the equation of line segment in parametric form using given points.

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1, 0) to…

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

Q: Evaluate the line integral (x+2y)dx + dy, where C consists of the path C from (0,0) to (3,0), the…

A:

Q: Find the line integrals of F = 4yi + xj + zk from (0,0,0) to (1,1,1) over each of the following…

A:

Q: Calculate the line integral [(of).do where f(x, y, z) = x ² ¹² + 4 xy² z yz с + е хуча and C is the…

A:

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: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

A:

Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

A:

Q: 5. Evaluate the line integral (r+2y) dr+x² dy where C consists of line segments from (0,0) to (2, 1)…

A: In order to solve this question by the formula of line integral .

Q: Evaluate the line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: a) Evaluate the line integral TM UTM in terms of 7 where F = cos yi+ rj + ye*k and C is the line F…

A:

Q: Evaluate the given line integral. I (y, –x) · dR, where C consists of 4y = x² from (-2, 1) to %3D C…

A: Line integration of the function

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 <…

A:

Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1)…

A:

Q: Calculate the value of the line integral fds where f(x, y, z)=e² and C is described by X C (x, y,…

A: The objective of the question is evaluate the definite integral.

Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…

A:

Q: Find the line integral of f(x,y,z) = -x+y+z over the straight-line segment from (1, 2, 3) to (0, −1,…

A:

Q: Find the line integral of F = 2√√zi-4xj + 3√yk, from (0,0,0) to (1,1,1) over each of the following…

A:

Q: Compute the line integral of the scalar function f(x, y) = /1+ 9ry over the curve y = x° for 0 <¤ <…

A:

Q: (a) Find the line integral of f (x, y, z) = -x + y + z over the straight-line %3D segment from (1,…

A:

Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: Find the line integral of f(x,y,z) = x+ y+z over the straight-line segment from (2,1,3) to (1, –…

A: Solution: f(x,y,z)=x+y+z

Q: Evaluate the line integral I of the one-form w = (y + z) dx + (x + 2) dy + 10z dz over the line…

A: Given: One-form ω=y+zdx+x+zdy+10zdz and the line segment joining 0, 0, 0 and (3, 1, 0). To find:…

Q: Find the line integral of f(x,y,z) = -x + y+z over the straight-line segment from (1, 2, 3) to (0,…

A:

Q: Use Green's Theorem to evaluate the line integral. y dx + 7x dy C: square with vertices (0, 0), (0,…

A:

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1,0) to…

A:

Q: (1) Evaluate the line integral of F (x, y) = (x – y, x²) over the line from (1,0) to (3, 2). |

A: evaluate line integral in following way

Q: Compute the line integral of the scalar function f(x,y,z)=2x^2+8zf(x,y,z)=2x2+8z over the curve…

A:

Q: Compute the line integral of the scalar function f(x,y,z)=2x2 +8z over the curve…

A:

Q: Evaluate the line integral Sa y dx +z dy, where C is the line segment from (4) (-1, 1, 2) to (2,3,…

A:

Q: 15. Evaluate the line integral J.(3xy* - 6xy ]dx + (4x°y³ - 3x?) dy, where C is any path from (1,2)…

A:

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

A:

Q: Use the Fundamental Theorem of Line Integrals to evaluate fo F·dR, where F(x, y) = (x²y² – 3x, r³y)…

A:

Q: Evaluate the line integral In(x + y) ds, z + 2 where C is the line segment from the point (1,0, –1)…

A:

Q: Evaluate the line integral ∮C x dy−y dx where C is a circular, closed path defined by x^2+y^2=16

A:

Q: 5, find the line integrals along the given path C. In 13. | (x – y) dx, where C: x = 1, y = 21 + 1,…

A:

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

A:

Q: Use Green's theorem to evaluate the line integral for the curve C given in the figure. [8y dx + 7x…

A:

Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

A:

Q: The line integral (x+/y) ds , where C is the line segment joining the points (0, 0) and (1, 1) , can…

A:

Q: Evaluate the given line integral. | (y, -x) dR, where C consists of 4y = x² from (-2, 1) to (2, 1)…

A:

Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

A:

Q: Calculate the value of the line integral fds where f(x,y,z)=e² and C is described by C (x, y,…

A: