Compute the scalar line integral xy ds where C is the part of the circle of radius 3, centered at the origin, that lies in the quadrant defined by the conditions x< 0 and y < 0.

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A: Given: fx,y=x-y To Find: Line integral ∫Cfx,yds over the unit semi-circle x2+y2=1, y≥0

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A: To find the line integral, obtain dS as follows.

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A: Given

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A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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A: Answer

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A: Solution: I=∫cxy4ds

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A: Solved below.

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Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 7y2 + 7z² and the…

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Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

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Q: Evaluate the line integral using the Fundamental Theorem of Line Integrals. (3y dx + 3x dy), where C…

A: Given line integral is: I=∫c3ydx+3xdy It can be rewritten as: I=3∫cydx+xdy                ....(1) As…

Q: Compute the line integral | (yze*v= + y° + z - 2x) dr + (xze*# + 2ry) dy + (rye#"= + x + 32²) dz,…

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Q: . Integrate f(x, y) = cos (x² + y²) (a) over the closed unit disk; (b) over the annular region 1 <…

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

Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: Compute the line integral (yze"y= + y² + z – 2x) dx + (xze"v² + 2xy) dy + (xye"y= +x+ 3z²) dz C…

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Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

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Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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Q: Find a parametrization of the curve x^(2/3)+y^(2/3)=8^(2/3) and use it to compute the area of the…

A: Finding the parameters: