The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed by the lines y = r, y = 5.x = 0 (anticlockwise direction) is given by +을-1 None of the answers is true O O OOO

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Q: Suppose F(z, y) = zyi+ (# – y)j and C is the triangle from (4, 0) to (-4,0) to (0, 4) to (4,0). (a)…

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A: Given integral I=∫Cydx+zdy-xdz  Curve helix C given by x=cosπt, y=sinπt, z=t  from 1,0,0 to -1,0,1…

Q: if a = 2, b = 6, c= 3 2. Let f(2) = x2 + iy? where x and y are the real and imaginary parts…

A: For the solution of the problem follow the next steps.

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Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

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Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

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Q: 2. Let R be the region inside the curve C :r=1+ cos 0 and to the right of the line l :r = 3 sec 0.…

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Q: 2. Evaluate directly the line integral fo a dy where C is the quarter-circle from (0, 4) to (4, 0)…

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Q: If C is the line segment from (1,3) to, (0, 0), find the value of the line integral: S(3y² i +3x}) ·…

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Q: 2 2 JEind. thePaints.an.th. sur face. Xy Z=1 that.are .... closest...t. the origin

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Q: Suppose F(x, y) = xyi + (x −y)j and C is the triangle from (4,0) to (-4,0) to (0, 4) to (4,0). (a)…

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Q: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

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Q: 3) Show that the line integral is independent of path and then evaluate the integral: S. sin y dx +…

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Q: If I, = Sx" cos x dr, by using integration by parts, prove that In = x" sin r + na"- cos r – n (n –…

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Q: 8. Evaluate the line integral x dx + xedy where C is the closed path along the triangle in the…

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Q: The shaded area shown in (Figure 1) is bounded by y axis and the curve y? = (1.44 – x) m, where z is…

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Q: Suppose F(x, y) = xyi + (x - y)j and C is the triangle from (4, 0) to (-4,0) to (0, 4) to (4, 0).…

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Q: 11 Let I= [[5 sin(v')cydx . By reversing the order of integration of I, we get:

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Q: Evaluate the line integral. 7ydx + 6z dy + x dz, r(t) = (2 +t,,1?) for 0 <t<1 (Give an exact answer.…

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Q: Find the length of x = In(sin y) from y = to y = . %3D

A: The arc length of a function is the length of a curve fy on an interval a, b given byL=∫ab1+f 'y2dy…

Q: 2 Sphere S to be the top half of sphere · x² + y² + 2² SS₁zdS /5 calculate the integral.

A: The given Surface is the top half of the surface x2+y2+z2=a2. To Evaluate: ∬zdS.

Q: 4| ind Volumes of のnen reo リュー! )ス"0) reten iegTon 1- dv - dzdy chy 1 Limik of 2:0> y2 Limik of y:…

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Q: Evaluate the line integral. 15y dx + 14z dy + x dz, r(1) = (2 +r,2.?) for 0 <i<1 (Give an exact…

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Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

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Q: Evaluate the iterated integral. 5 6 7 ||| ? +y² + 2) dx dy dz -5 0 0 5 6 7 | || (1²+y² +²)dx dy dz =…

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Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: 1. What should be A for the path independent of (2,4) ry + ) 2Ay – x dy y? dx+ (1,2) Moreover…

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Q: The value of the line integral S(2xy²dx + 2a?ydy + dz) along a path joining the origin and the point…

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Q: The path integral fv· dr, where v = (sin y, x – cos y) and C is the perimeter of the triangle formed…

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Q: 7. Use contour integration to evaluate (a) dr x²+x+1² de (b) 3+2 sin

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Q: Express the length L of the curve r = sin3(0), 0 < e < as an integral but do not evaluate it. /7 de

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Q: Q4: State the Fundamental Theorem of Independent of Path and Morera's Theorem. Why can't apply these…

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Q: The area of the surface generated by rotating the curve y = 1 = cos(3x), where 0 ≤ x ≤ , about the…

A: Let's find Area of surface,when rotated about x axis.

Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

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Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…