2. Consider the work integral (y- x²) dr + (1– x) dy. Consider the following two paths that start at (-1,1) and end at (3,9): • (-1+4t, 1+ 8t), 0

Q: 4. Let D = y²z°ãx + 2xyz³ ày + 3xy?z² đz pC/m² in free space. a. Find the total electric flux…

A: Solution:-

Q: 1. Calculate the integral 1 y-stnx)dx + cosy dy a) With directly (classical), b) With the Green's…

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

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: Use Green's Theorem to evaluate the line integral |(v - x)dx + (2x – v)dy for the given path. C: x =…

A:

Q: 19. Find. thedivergen ce. and.cur..4the fellowiny vecter. field: a.. F = Xej+. y.e... b. Ês ĕsiny i…

A: We need to find the divergence and curl of the following vector fields. a. F→=xeyj+yezk=(0,xey,yez)…

Q: 43.) Show by checking cross partials that F = (4x³y² – 2xy³, 2x*y – 3x²y² + 4y³) is conservative Use…

A:

Q: Evaluate the integral (2x – y) dx + (x + 3y) dy along the path C. C: x-axis from (0, 0) to (0, -3)…

A:

Q: Find the solution in the form of Fourier integrals: U4-3uzz = 0, |u(x, t) bounded as x → ±0, sin r…

A: We are given the following second order partial differential equation : ut - 3uxx = 0  ;  -∞ < x…

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: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

Q: Use Green's Theorem to evaluate the integral (y - x)dx + (2x - y)dy for the given path. C: x = 2…

A: Definition used -                                According to the green theorem -…

Q: Evaluate the line integral (-3x+y)dx + (x + 3y)dy, where C lies along the x-axis from x = 0 to x = 6

A:

Q: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: Q.4 Show that in the following problems, the line integrals are independent of path of integration…

A:

Q: (3) Evaluate the line integral of the first type fez2 ds, where C: x = cost y = sint where 0 ≤ t ≤…

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. √(²x- (y - x)…

A:

Q: 9. let C G TR? be Simple Close d curve bounding the positively orierned a reyi'on D. IF Area cO)=|…

A: Given that, Area(D)=∫Cx2+2xy+2y+eydx+∫CAx+x2+xeydy

Q: 1. Show that the problem may be formulated in terms of the velocity potential o(r, 0) satisfying 6,…

A:

Q: Verify Green's Theorem by evaluating both integrals | y2 dx + x2 dy dA ду for the given path. C:…

A:

Q: 3) S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz - Calculate the…

A: Let's find.

Q: , (xy + 2)dV, 27. Calculate where B = {0 < x < 2, 0 <ys1, 1< z < 3} as an iterated integral in two…

A: Consider the following integral: ∫∫∫Bxy+zdVB=0≤x≤2, 0≤y≤1, 1≤z≤3 Consider the first way:…

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

A:

Q: Consider the curve segments: 1 - to x = 4 and 4 1 X = -to x = 16. 16 S1: у %3D = x² from x = S2: y =…

A: Given that:

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

A:

Q: 17. Evaluate the line integral xe" dx +y sin yªdy along the triangular path consisting of the line…

A: Consider the given integral. I=∫Cxex2dx+ysiny2dy The given points are 0,0,2,3,1,0,0,0. Now, draw all…

Q: Given F = (2xze*²z – 4, cos z, x²e*z – 3ycos?z sin z) 1. You are to show that the line integral S.…

A:

Q: Use Green's Theorem to evaluate the line integral () in(x²+y?) oy 2 arctan Y dx + Inx2 C: x = 9 + 6…

A: Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a…

Q: 1. Let F(x, y, z) = (2re²*+3», 3e* +3v +2/E, ). 2.x cez²+3y a. Show that F is conservative using its…

A:

Q: What is the value of the line integral on the field 5xy? 5æ?y F(x, 3) = ()i+ ( 2 along any path from…

A:

Q: Q5 Use Green's theorem to evaluate the line integral (cos.x+2y)dx+(x – sin y)dy C where C is the…

A:

Q: Find the value of the line integral 6xy dx + (3x² + 4y2)dy, where C is an ellipse 16 + = 1 from (4,…

A:

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √((x-x) (y -…

A:

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

A:

Q: Q#03:Use Green's theorem to evaluate the line integral x³y² dx+ (cos5x – 2e2*y³)dy, where C is the…

A: According to the given information, it is required to evaluate the line integral using Green’s…

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

A:

Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: Q21 Verify Green's theorem for $. (xy² + x²)dx + (4x – 1)dy where Cis shown in the figure by (a)…

A:

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

A:

Q: Evaluate the line integral di the path over C from to Q(2,4) P(O,) where F(xy) 2xy°2+3y5 13D to ネソーメ…

A:

Q: Use Green's Theorem to evaluate the line integral. et cos(2y) dx 2ex sin(2y) dy C: x2 + y2 = a?

A:

Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

A:

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

A:

Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

A:

Q: Use Green's Theorem to evaluate the line integral below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0…

A: Given integral is ∫Cx2-y2dx+7xy dy where C: r=1+cosθ,  0≤θ≤2π To Use: Green's Theorem to evaluate…

Q: Verify Green's Theorem by evaluating both integrals ам √₁ y ² dx + x² dy = √₂√ √ (³x - dA ax ду for…

A:

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x - y)dy for the given path. C: x =…

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: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…

A: