1. Give iterated integrals for , F · dS where F(x, y, z) = (x, x², 2z) and S is the part of the graph ofz = x²y over the triangle whose vertices are (0,0), (1,0) and (0,2). Assume S is oriented down. [DO NOT EVALUATE]

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: Suppose f(x, y, z) = (a) As an iterated integral, 1 x² + y² + z² and W is the bottom half of a…

A: Triple integral

Q: Evaluate the line integral by the two following methods. fwox xy dx + x²y3 dy C is counterclockwise…

A: Since, we have to evaluate the line integral given by:-I=∮C xy dx + x2y3  dy -(i)Our aim is to solve…

Q: 2) Evaluate the following line integral: . 0+z)dx + (x + z)dy + (x + y)dz where C consists of the…

A: C1: (0,0,0) to (1, 0, 1)x-01-0=y-00-0=z-01-0=tx=t, y=0, z=tdx=dt, dy=0, dz=dtI1=∫01[(0+t)+(t+0)]…

Q: 1- Assume that x,y ER and z=x+ iy € C. Calculate the following integrals on C = {z:|z] = 1} contour.…

A: Residue theorem: If C is positively oriented simple closed curve and a1, a2,..., an are the point of…

Q: Evaluate the given line integral. | (y, -x) · dR, where C consists of the uppder part of x2 + y? = 1…

A:

Q: 2- Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

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: 1- Assume that x, y ER and z = x+ iy e C. Calculate the following integrals on C = {z: |z| = 1}…

A: Cauchy integral formula

Q: Evaluate the triple integral. I/| (x - y) dv, where E is enclosed by the surfaces z = x2 - 1, z = 1…

A:

Q: 1. The integral of J, \z|dz along any closed path y is 0.

A: As per our guidelines, we suppose to answer only one question in case of multiple questions posted.…

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: 1. Evaluate the given line integral, I (-y,x – y) · dR, where C is the upper part of 4.x? + 9y? = 36…

A: we have to find the line integral  ∫C-y,x-y.dR→ where c is part of the ellipse 4x2+9y2=36 from…

Q: 2- Assume that x, y € R and z = x+ iy e C and answer the followings. Calculate the reel integrals…

A: Consider the contour which is given in the question. We have to evaluate ∫0∞1x2+1dx in the given…

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy = / / dA ax for the given path. C:…

A:

Q: Verify Green's Theorem by evaluating both integrals ax dA ду for the given path. C: rectangle with…

A: From: (0, 0) to (5, 0)y=0, dy=0∫ y2 dx+ x2 dy =0From: (5,0) to (5, 9)x=5, dx=0∫09 x2 dy= ∫0925…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: y 3 2-…

A:

Q: Find the line integral of f(x,y,z) = X+ y+z over the straight-line segment from (2,4,3) to (1,1,1).…

A: Line integral

Q: (b) Evaluate each of the following line integrals: (1) xds, where C is the portion of the curve x…

A:

Q: 2- Assume that x, y ER and z = x+ iy € C and answer the followings. Calculate the reel integrals…

A: Cauchy lemme

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: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 1 from…

A:

Q: Use the Fundamental Theorem of Line Integrals to calculate d exactly. 7-7+4y²f arqund the top of the…

A: Given

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

A:

Q: 2) Evaluate the following line integral:S. (v + z)dx + (x + z)dy + (x + y)dz where C consists of the…

A:

Q: 1-) Assume that x, y E R and z = x + iy e C and answer the followings. Calculate the reel integrals…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r ±1 and…

A: According to cauchy’s integral formula for any region C,

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: У 3…

A:

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: 1) Evaluate the triple integral SS, f(x,y, z)dv : A) f(x,y, z) = 2x + y – z, Q = {(x,y, z): 0 < x, z…

A: A) Set up the triple integration using the given information.Here dv represents dxdydz.…

Q: 1-) Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

A: Given: (a) ∫-∞∞ x2x4+1 dx (b) ∫-∞∞ x2(x2+1)2 dx We have to calculate the (a) and (b)

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: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 4 from…

A: Given  ∫C(-y,x-y).dR→ where C is upper part of circle  x2+y2=4 from (-2,0) to (2,0).   Note-As per…

Q: 2) Let C denote the positively oriented boundary of the square whose sides lie along the lines x =…

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: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

A:

Q: Evaluate the given line integral. | (y, –x) · dR, where C consists of the uppder part of x² + y? = 1…

A:

Q: let C denote the polygonal line from (0,0) to (1+) evaluate the integral on Cf (z) y-x-13x2 where…

A:

Q: 1. Evaluate the given line integral, | (x – y, y) · dR, where C is the left part of x² + y? = 1 from…

A:

Q: 2) Evaluate the following line integral:S, (y + z)dx + (x + z)dy + (x + y)dz where C consists of the…

A:

Q: B. Verify Green's Theorem by evaluating both integrals involved in that theorem when F = (x² – y) i+…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the closed region D. The Green's…

Q: 1- Assume that x, y ER and z = x + iy E C. Calculate the following integrals on C = {z: |z| = 1}…

A: By residue formula we can solve the problem

Q: Suppose that f(æ, y) = 7, and D = {(x, y) | x² + y² < 1}. Then the double integral of f(x, y) over D…

A:

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: f(x,…

A: the double integral formula  ∫x1x2∫y1y2f(x,y)dydx the value of y varies from 0 to 3 and the value of…

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

A:

Q: 2- Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel integrals…

A: a)The given integral is,  ∫0∞1x2+1dx

Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

Q: Evaluate each of the following line integrals. x dy – y dx, 2n <t< 4TT (a) c(t) = (2 cos(t), 3…

A: According to the given information it is required to calculate the line integral. For part (1)

Q: Let f(z)=4Re(z) and C be the line segment connecting 1+i to 0. Then the integral of f over C is…

A: Given function is fx=4Rez and C be the line segment connecting 1+i to 0 We have to find the integral…