Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of radius 10 in the xz-plane with center at the origin in the quadrant x > 0, z < 0, oriented counterclockwise when viewed from the positive y-axis. (Use symbolic notation and fractions where needed.)

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Q: Assuming that C is the counterclockwise oriented boundary curve of the unit square in the first…

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Q: 5) Evaluate the integral (e* - y) dx + (sin y + x)dy using Green's theorem where Cis bounded by y =…

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Q: The area of the surface obtained by rotating the curve y = 1<xse about the line x = 32 is ** 12 (32…

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Q: 4. If the curve y = In x between x = 1 and x = e is rotated about the y axis, which integral below…

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Q: (a) Calculate the iterated integral 3 7/2 SS(v+y° cos x)dx dy -3 0

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Q: Evaluate the iterated integral. (x + y²) dx dy THERE

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Q: Calculate the integral I = | (2a – y) dx - (a – y) dy where L is the curve represented as x = a(t –…

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Q: 6) Find the length of the arc of the curve y² =x ³ from (1, 1) to (2, 2 v2) twice using two…

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

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Q: Calculate the following integrals. In both cases the curve C has a counterclockwise direction: 4.1…

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Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

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Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r ±1 and…

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Q: Evaluate the line integral f. 4y dx + z² dy + (16 – x²) dz over the quarter of the circle of radius…

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Q: 13. compute the integral // e10(x-y)²+8zy dædy over the ellipse & := {(x, y) ; 5x² + 5y² < 6xy+ 1}.…

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Q: Evaluate the line integral fe 3y dx + z? dy + (25 - x) dz over the quarter of the circle of radius 5…

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Q: 4. Find the value of the integral 223 + 5 'zp- c (z – 1)(2² + 9)* taken counterclockwise around the…

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Q: 7. Evaluate the integral I | sin(9.r² + 4y²)dA by hand, using an appropriate change of variables,…

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Q: Q.01: Use Green's theorem to evaluate the line integral £ e2*sin2ydx + (e²*cos2y)dy, where C is the…

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Q: Apply Green’s Theorem to evaluate the integrals ∮(3y dx + 2x dy)C: The boundary of 0≤ x ≤π, 0 ≤ y ≤…

A: According to Green's theorem - ∮Pdx+Qdy = ∬D dQdx-dPdydxdy          ...............(1)Given integral…