Evaluate P (3x + 4y) dx + (2x – 3y) dy where 'C is the circle x?+y = 4.

Q: -z Q2. In the circle |z| = 1, Find the upper bound for 9z4+3z²+2l

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Q: Find the arc length of the graph by partitioning the x-axis.   9y2 = 4(1+x2)3 , from x=0 to x=4√2…

A: Given: 9y2=4(1+x2)3  from x=0 to x=4sqrt(2)

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: Find the tangent line to the given circle as directed. x² + y² + 10x – 6y – 2 = 0 parallel to y =…

A: Equation of the circlex2 + y2 +10x -6y -2 = 0⇒x2 + y2 + 10x -6y -2 + 25 - 25 + 9 -9 = 0           .…

Q: Integrate f(z) = 1 Z³-Z4 clockwise around the circle C: |z| 1 NIT 2

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Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

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Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

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Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

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Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(1)

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: 5. Tangent B. Determine the center and radius of each circle: 6. x2 + y2 =16 7. (x-2 )2+ y2 - 13 8.…

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Q: Q2 Calculate 8- z dz, z(4- z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Evaluate Iz = y", 2ry ) · d7 where C3 is the arc of the curve x = 3 – 2y that extends from (7, –2)…

A: we have to evaluate the following

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

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Q: Q2 Calculate 8 - z dz, (4- | where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Q2 Calculate 8-z dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

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Q: Find the arc length of the graph of y^2=4x^3, between points (0, 0) and (2, 4sqrt(2)).

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Q: 16 6xy ds, where C is the right half of the circle x² + y² = 4. Evaluate the line integral

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Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

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Q: Find the length of the curve y = In(1 – x), 0sxs.

A: Given: y=ln(1−x2)0≤x≤12

Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

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Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

Q: Find the arc length of the graph by partitioning the x-axis. y =2/3(x2 + 1)3/2, from x = 2 to x=7

A: The arc length of a curve y = f(x) over an interval [a, b] is given by the formula

Q: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

A: We will find out the required value.

Q: Find the arclength of y = 3x2 -5 on x is greater than or equal to 0 and less than or equal to 2

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Q: 4. Evaluate / (z – 2) dz where C is the lower half of the circle |2 – 2| = 4.

A: Note: According to bartleby guidelines we have to answer only first question please upload the…

Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Compute ž dz +y1 z dz, +72 and where +Y1 is the segment from 1 to -1, and +y2 is the arc on the unit…

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Q: Determine the osculating circle of the helix defined by y = x^3 − 3x + 1 at x = 1.

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Q: Find the length of arc from (2,1) to (4,4) of the curve x = 2√y

A: Let us consider curve x=g(y). The arc length of graph of g(y) from point (a, f(a)) and b,f(b) Arc…

Q: Find the length of the arc of the curve x2 = (y − 2)3 from P(1, 3) to Q(8, 6).

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Q: Evaluate fc 2x ds, where consists of the arc of the parabola y= x2 from to followed by the vertical…

A: The given line integral is ∫C2xdS where C is the arc of the parabola y=x2 from (0,0) to (1,1) and…

Q: Let C be a circle with |z - i| = 3 travelled once in counterclockwise direction. Evaluate: 5z3 + 3z2…

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Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

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Q: Express the circle specified by a = 2 cos(0) y = 1+2 sin(0) in Cartesian coordinates and find the…

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Q: Find the arc length of the graph by partitioning the x-axis. y=1/3 (x2 +2)3/2 , from  x = 3 to x =…

A: Given: The function y=13x2+232  fromx=3 to x=4

Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4,…

A: The answer is as follows:

Q: Express you answer in Mdx + Ndy = 0. 1. Circles whose center is passing through y = 4x %3D

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Q: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

Q: Find the exact length of the curve. y = (1 + x*,3/2, OSxS 5

A: The curve is y=231+x232 , 0≤x≤5

Q: Let C be the circle |z| = 4 traversed once in the positive sense (counter %3D clockwise). Compute :…

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Q: 8. centered at Which of the following equations represents the circle with radius F 16x2 + 16y2- 16x…

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