1. Let S be the piece of z = 4 – - y² that lies above the square {(r, y) : 0

Q: Evaluate the line integral, where C is the given curve. xy dx + (x − y) dy, where C consists of…

A: In the above line integral there are two segments which needto be seperated. First (0,0) to (1,0) so…

Q: Find the line integral of x ds over C where c is the line segment from (1,0) to (0,1) using two…

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

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Q: find the line integrals along the given path C. ∫C (x - y) dx, where C: x = t, y = 2t + 1, for 0≤ t≤…

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Q: Calculate the iterated integral. 3 Vs+t ds dt

A: Consider the iterated integral

Q: Evaluate the line integral, where C is the given cu curve. (x + yz) dx + 2x dy + xyz dz, C consists…

A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

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: 3. Compute , xe*ydA where R is the rectangle 0 <x< 1,1< y< 2, using iterated integrals in both…

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

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Q: 1- Assume that x, y € R and z = x + iy € c.Calculate the following integrals using the given contour…

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Q: Evaluate the line integral, where C is the given curve. (x + 8y) dx + x2 dy, C consists of line…

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

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Q: Consider: dr, C: r(t) = (t, t²), te[0,1] Which one of the following "regular" integrals represents…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

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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 line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: Is dz

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Q: Eval u ate the double integrals overs the indicated re sions り ye JA, R: the region bonnded by the…

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Q: 22 Calculate the value of the integral over the following C curves. a) C:l2+1| = 1 1, %3D c) C:l오+1…

A: we have ∮Cz2z2-1 a C: z+1=1⇒C:x+iy+1=1⇒C:x+1+iy=1⇒centre is -1,0 and radius is 1 Thus, only pole…

Q: Evaluate the integral. y In(x) dx, y > 0

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

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3…

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Q: Evaluate the line integral, where C is the given curve. (x + 9y) dx + x² dy, C consists of line…

A: To evaluate the line integral, consider the curveC1 consisting of the line segment from0,0to9,1. The…

Q: Evaluate the line integral given in the figure below

A: Given question is belongs to the vector calculus and from the line integration we have to integrate…

Q: Evaluate the line integral, where C is the given curve, (x + 9y) dx + x2 dy,  C consists of line…

A: Consider the line integral,

Q: Compute the following integral: ez -dz z(z – 3) where y = {z : |z| = 2} positively oriented.

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Q: 5. Compute the following double integrals: ye*y dA where R is the square -1 <x < 1, 0<y<2.

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

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Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Note: According to our guidelines We’ll answer the 3 subparts of the question since the exact one…

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

A: Given

Q: Evaluate the integral, z' dv where, E lies between spheres2+y += 2 and +y += 3, for z 2 0

A: According to question,E lies between spheres,x2 + y2 + z2 = 2,andx2 + y2 + z2 = 3,x≥0

Q: Calculate the double integral: S,(y + xy – 2) dA where R= [0,2] x [1,2].

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Q: Solve the problem in a paper and upload as a pdf document. .3 Evaluate the integral SIT w?yz+v² xz +…

A: Solution: The objective is to evaluate the given integral

Q: Evaluate the given line integral. (y, -x) · dR, where C consists of the uppder part of 2² + y? = 1…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y² dz, C is the line segment…

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Q: 1. Let S be the piece of z = 4 – x² – y² that lies above the square {(x, y) : 0 < x < 1, 0 < y < 1}.…

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

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Q: Evaluate the line integral along the curve C. S-s - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O…

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

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Q: Evaluate the line integral along the given path. (4x-7y)ds C:r = 7ti+6tj, 0 ≤ y ≤8 O-454/85 O-444√85…

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Q: Set up the iterated (triple) integral for the integral ]]] xy¹z³ dV where S is the tetra- S hedron…

A: We will find limits of variable and then find value of integral

Q: 4. Evaluate the double integral D where D is enclosed by the curves y = a², y = 3x.

A: First we will draw the graph for given curves from that we will find the limits of x,y as shown…

Q: Evaluate the double integral. dA, D = {(x, y) |0Sx< 5,0 < ys Vx} x2 + 1

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Q: Evaluate the line integral along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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Q: Evaluate the line integral, where C is the given curve ʃc (x+9y)dx +x2dy, where C consists of line…

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

A: Consider the given figure in the question. We have to evaluate I=∫x=0∞1x3+1dx in the given contour…