Evaluate the surface integral - [[F-ds when I = F(x, y, z)= e(4xi+j) and S is the graph of shown in (1+x²-y²), 0≤x≤ 1,0 ≤ y ≤1,

Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

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Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: 6- Evaluate the line integral fe F dr, where F = [ry, yz, r2] and C is the boundary of the…

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Q: 6. Evaluate the line integral F · dr where F = (x³ —y¹, ex²+z², x² – 16y² z²) and C is the curve x²…

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Q: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

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Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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Q: Dat

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Q: = Jó 7xds where C consists of the arc C₁ of the parabola y 3x² from (0,0) to Compute the integral I…

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Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

Q: . Evaluate the line integral where F x² + y² = 4 in Q1, Q2, and Q3. - (1, 2y) and the pathway C is…

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Q: Consider that C is a curve given by the triangle of vertices (0,0), (2,0) and (2,1), oriented…

A: We will evaluate the given integral.

Q: Show that Jo edx + (xe + sinz)dy + ycoszdz is independent of the path and evaluate the integral if C…

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Q: 3. Evaluate the line integral (3ry² + 6y) da, where C' is the path traced by first moving from the…

A: The given problem is to evaluate the given line integral of (3xy2+6y) over the given path C which is…

Q: 2. Triangle FGH with verlices F(1,8), G(5, 7), and H(2, 3): y-x F' G' H' - 177

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Q: Suppose F(x, y, z) = (ex, 2³, y² + 2) (a.) calculate V x F (b.) let C be the line segment from (0,…

A: (a.) To find: .(b.) To find: , where C is the line segment from (0, 0, 0) to (1, 2, 3).

Q: Evaluate 7. dr

A: We will use F→.PQ→ to evaluate integral

Q: 6. Show that the line integral fry²dx + (x²y + 2x)dy around an rectangle depends only on the area of…

A: Answer :-

Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: 1. Evaluate the integral If. (430 R (4x + 16y)dA, where R is the parallelogram bounded by the lines…

A: To find the given integral , we can change the given integral in  terms of 'u' and 'v' .

Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

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Q: - {z,y, 2)| 2 2= > 0} //| dpdød0 set Consider the 3D domain W = Calculate | a2 + y? + z² d(x, y, z)…

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Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

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Q: Let f(x, y, z) = eª + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A: Given: The function is fx,y,z=ex+zy2 and let C be a straight line that will connect the points 4,2,1…

Q: Evaluate the line integral where C is the curve made up of the straight line segments from the…

A: We will find parametric equations of line segment and then find line integral