The following equation descnbes a semieilipse C,: 7t)= -2 st T2 %3D if F =(0, 2z, 4yt1> calculate the line Integral S F. d? %3D

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Q: Evaluate the line integral ry dz for C : r(t) = (e , et+1)", te'), 0 <t<1 and then repeat with -C in…

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

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Q: Use a calculator or CAS to evaluate the line integral correct to four decimal places. x sin(y + z)…

A: find the explanation below

Q: Evaluate the line integral, where C is the given curve. Sc (2x + 9z)ds C: x = t, y = t2, z = t 3, 0…

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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…

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

Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Calculate the line integral £ (6² + &z + 5y + 4) dz + (-5z – 39² – 10y – 10) dy. where Cis the…

A: Calculate the integral: ∮C6x3+8x+5y+4dx+-5x-3y3-10y-10dy C: Unit circle x2+y2=1

Q: The foilowing describes a para bolic path C: Pt) = (t, 2, 1-t?) %3D if F = (32, x + y+Z, 2x >,…

A: The given problem is to evaluate the line integral of the given vector field over the given…

Q: Evaluate the line integral along the curve C. J (3x - 2y) ds; C is the line segment r(t) = (2t,t)…

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Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: So(3y² i +3xj)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate the line integral So 7y dr + 3x dy where C is the straight line path from (2, la 7uda + 3z…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: Evaluate the line integral, where C is the given curve. Sc xy² ds, C is the right half of the circle…

A: Use parametric  method to solve

Q: valuate the line integral Scy da +a dy where C is the parameterized path a = t2, y = t°, 1<t<4. Scy…

A: We have to find the given integral.

Q: Perform the line integral f, dī × V with V = Voêg and where C is the contour shown below y 1 C -1 1…

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Q: 31 Evalvate the line integral gy lx + 8z dy tx dz, r(t) = (2+ t +3 for Ja9ydxt8zdyt xdz =

A: The line integral ∫C9ydx+8zdy+xdz, r(t)=2+t-1,t3,t2 for 0≤t≤1. We have to evaluate this integral.

Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

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Q: Evaluate the line integral, where C is the given plane curve. | xy* ds, C is the right half of the…

A: Use parametric to solve

Q: Evaluate the line integral, where C is the given curve. Lexy² ds, C is the right half of the circle…

A: Solution: I=∫cxy4ds

Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

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Q: Evaluate the line integral, where C is the given curve. хуеу2 dy, C: х %3D 3t, у%3D 2t?, = 2t3, 0st<…

A: x=3t, y=2t2,z=2t3

Q: Evaluate the line integral ∫Cx2ds, where C is a the curve given by the equation y=f(x)=lnx, 1≤x≤e.

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Q: Please solve the following given line integral: Sc 3x?yz ds where C is the parameterized curve that…

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Q: Evaluate the line integral - y)dz + (1+ } + æ*)dy, where C is the circle of radius 1 centered at the…

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Q: Evaluate the line integral, where C is the given curve. | xy? ds, C is the right half of the circle…

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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: 2. At what point on z = a? + y? is the tangent plane parallel to 3.r – 4y + z = 7 ?

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Q: Use Stoke’s Theorem to evaluate the line integral ∮C(x+z)dx +(x−y)dy +xdz. The curve C is the…

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Q: Evaluate the line integral T, (“+y) dx + 4 ry dy where L is the path, -> r) = (3 t, 2) with 0 <t <1.…

A: We evaluate given integral

Q: Calculate the line integral a) |y ds, C:x =ť², y = 2t, 0 <t < 3 C

A: Use parametric to solve

Q: : The curve C is intersecting by 12r² +9y? = 36 cylinder and - V3r plane from the point (0, 2,0) to…

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Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: Evaluate the line integral (x – y°)dæ + (1+ y +z*)dy, where C is the circle of radius 2 centered at…

A: Hint: By green's theorem in a plane  If fx,y,gx,y be continuous in a region E of xy-plane bounded by…

Q: find the Jolume of the salid genereted by revaling- the curve 4t'qy=36 between y = 0. and g=2 Gbout…

A: The objective is to find the volume of the solid about y-axis.

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

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Q: Find the area of the surface that is generated by revolving the portion of the curve yx' between x0…

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Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t³, t2) for 0 <ts 3

A: Given: From the above function, the following can be written,

Q: valuate the line integral J xev% ds where C is the line segment from > (1, 1, 1). This yields:

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Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

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: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

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Q: Evaluate the line integral. e ds where C is the curve given by x=2t, y=3t, 0<t<2

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Q: Let F(x, y) that starts at (0, 0)and ends at (1, 2). (6æ? + 4y) 7 + (4x + 3) j. Calculate la F . dř,…

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Q: y = x, y = 2x, about the line x = 2 can be computed using the method of disks or washers via an…

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Q: The area of the surface obtained by rotating the curve * = 3t, y = 65 – 4t 5 st36. about x -axis is…

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