1. Integrate P (3)*dz, C: clockwise unit circle centered at (0, 0).

Q: Evaluate the line integral -y dx + z dy + 2x dz, where C is the helix by 7(t) = (cos t, sin t, t),…

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Q: ind | Idy + ydz, where C is the arc of the curve y = e for 0<z < 1

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Q: Evaluate COS Z -dz , where C is the circle |z – 1| = 3. (Integrate counterclockwise around C.)

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Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices ±1, tj clockwise.

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Q: Evaluate the line integral [(x+ y)dx+(x - y)dy, where C is the arc of the parabola y = 2x from (0,…

A: The integral in the form ∫CM(x,y)dx+N(x,y)dy involves the integration over a specific path C. In…

Q: Compute the line integral (х — y) dx + xe x dy, where C is the closed curve consisting of two line…

A: line integration

Q: Evaluate the integral x² dx + y? dy where C consists of the arc of the circle x2 + y² = 4 from (2,0)…

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Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: dr Let A be the area of a circle with radius r. If dt 5, dA when r = 1. dt find

A: A is area of circle of radius r A = πr2 Differentiate the equation with respect to t

Q: Evaluate the following line integral | 2ry da + 42°y² dy along positively oriented circle with…

A: Let C is a counterclockwise oriented simple closed curve with the interior region R. According to…

Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: If C is a circle of radius 8 centered at the point ( 0, 5 ), then evaluate pain(2dr + (11æ sin(y*…

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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: 4. Evaluate the line integral 6. x²y dx – xy² dy where C consists of the arc of the circle 16 = x² +…

A: Given equation of circle is  x2+y2=16x2+y2=42 radius is 4 We have to calculate line integral ∮ cx2y…

Q: Evaluate cos z dz , where C is the circle |z – 1| = 3. (Integrate counterclockwise around C.)

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Q: T 9. TO = PO nrre CHOICE 10.Sector of a circle is the region bounded by two radii and their…

A: We have to identify true or false.

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

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Q: Given x = y²+2y 8 -In(y + 1), find the arc length for 0 ≤ y ≤3

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Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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Q: integrate ƒ(x, y, z) = sqrt(x2 + z2) over the circle r(t) = (a cos t)j + (a sin t)k, 0&lt;= t…

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Q: Evaluate the line integral (2 - u) dz + (3 + æ) dy] where C is the parabolic arc = a² from (0, 0) to…

A: We have to evaluate the line integral.

Q: Find the area of the region enclosed by the curve r = 2+ cos (20). (1.) (3,( Bu Die Aya Yard 97…

A: To find the area of the region enclosed by the curve r=2+cos2θ

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: Integrate ƒ(x, y, z) =-2x2 + z2 over the circle r(t) = (a cos t)j + (a sin t)k, )  0&lt;=…

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Q: Evaluate the double integral // (x² + y² + 3) dA R over R: the circle centred at the origin (0, 0)…

A: Double Integration problem.....

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dr where C is the line…

A: Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 3

A: Given: x=y2+2y8-ln(y+1) The arc length is: L=∫ab1+dxdy2dy Now, dxdy=dy2+2y8-ln(y+1)dy…

Q: Find the arc length from (x1, y1) to (x2, y2) on the graph of f(x) = mx + b.

A: Given Data The first point on the graph is (x1, y1). The second point on the graph is (x2, y2). The…

Q: C is the part of the circle = 1 in the first quadrant, find the following line integral with respect…

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Q: 29. Let C be the quarter of the unit circle in the first quadrant, traversed coun- terclockwise from…

A: Explained below

Q: e? dz, calculate give integral. When C is a circle z= 2 (z – 1)

A: Introduction :

Q: Evaluate the line integral ſc(4y+ tan? x)dx + (6x – evsin´y)dy over curve C that is the circle x2 +…

A: Green's theorem problem....

Q: Calculate the following double integral as the inside of the circle R: x² + y² = 1.

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Q: 10. (~Ch16 Review #17) Use Green's Theorem to evaluate | x?y dx – xy? dy where Cis ,2 the circle x2…

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Q: Evaluate the line integral § (x − y) dx + (x + y) dy, where C is the circle with center the origin…

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Q: B. Evaluate sin z z²+j2z dz, C the boundary of the square with vertices +1, tj clockwise.

A: Evaluate the integral ∮Csin zz2+j 2z dz, where the path C represents the boundary of the square with…

Q: Let M(x, y) = y - cos y and N(x, y) = x sin y. Use the Green's Theorem to calculate the line…

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Q: Find the arc length of y = e* over [0, 1].

A: We have to find the arc length of y=e^x over[0,1]

Q: #3. Evaluate the line integral O (y dx- x dy) where C is the positively oriented circle with center…

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Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

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Q: ) + () 2 If C is the part of the circle = 1 in the first quadrant, find the following line integral…

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Q: By revolving the semicircle x = r cos t, y = r sin t. (0 ≤ t ≤ π) about the x-axis, show that the…

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Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

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Q: 1. Integrate P(2)dz, C: clockwise unit circle centered at (0, 0). C

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…