37. f dx + g dy; C is the path consisting of the line segment from A(6, 4) to B(1, 2) followed by the line segment from B(1, 2) to С(3, 6).

Q: Compute ye*ds where Cis the line segment from (1,2) to (4,7). .A 16 34 e4

A: According to the given information, it is required to calculate the value of integral.

Q: Calculate the length of the path over the given interval. c(t) = (3t2, 4t*), 1<t< 4

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Q: Evaluate the line integral 6ydx + 4xdy where C is the straight line path from (2, 3) to (5, 5). Jc…

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Q: C is the line segment from (4, 2) to (0, 0) followed by the line segment from (0, 0) to (-4, 2).…

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Q: O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

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

Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x = 1+2t, y=5+15t, z=-2+6t,…

A: given : the equations of two skew lines are: L1: x=1+t, y=1+6t, z=2tL2: x=1+2t, y=5+15t, z=-2+6t D…

Q: 20. Evaluate l Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: 2. Evaluate S. 3x – 6y ds for C is the line segment from (6,0) to (6,6).

A: Solution

Q: Consider the path r(t) = (4t,2t 2 ,2lnt) defined for t > 0. Find the length of the curve between the…

A: Given the path r(t) = (4t, 2t2, 2ln t), t&gt;0. Find the length of the curve (4, 2, 0) and (20, 50,…

Q: Calculate the length of the path over the given interval. c(t) = (9t + 1,9 – 9t), 0 <t < 2

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

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Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

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Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

Q: Suppose that these two lines are the paths of two particles. If t and s measure ime in seconds, and…

A: We have given the equations of two lines : l1 : x,y,z=2+2t,8+t,10+3t l2 : x,y,z=5+s,12-2s,17-s…

Q: Show that fdx + gdy = S 36x°y?dx + 18yx*dy is independent of path: (3,6) (-2,4) (3,6) 2,4) C(3,6)…

A: The vector field is conservative if the components satisfy the test ∂P∂x=∂Q∂x. If the field is…

Q: 20. Evaluate J Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: Sc 7ydx + 3z dy where C is the straight line path from (2, 4) to (4, 7).

A: The parametric equation of the straight line between the points (a,b), (c,d) is x-ac-a=y-bd-b=t,…

Q: Evaluate ſc(x – y) ds over the path C: F(t) = 4tỉ + 3tj for 0 <t< 2.

A: Given: The curve C: r→t=4ti→+3tj→ for 0≤t≤2 To Evaluate: The integral∫Cx-yds

Q: 21. Reflect in the y-axis. 5- 4- 2+ х -2 -3+ -4 T'(2, 2), V'(4, 1), W'(5, 4), X'(0, 4) b. T(-2, -2),…

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Q: (a) Compute S ædx + ydy + (x + y – 1)dz where C'is the line segment from (1, 1, 1) to (2, 3, 4).

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Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Find y dr + (x + 2y) dy, where C is the piecewise linear path from (0, 1) to (3,0) to (4, 5) to (1,…

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Q: C is the line segment from (4, 2) to (0, 0) followed by the line segment from (0, 0) to (-4, 2).…

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Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z 2t L2: x=1+2t, y=5+15t, z= -2+6t,…

A: Two lines in space can be skew, parallel and intersecting. Lines are skew if they are neither…

Q: Compute the length of the path r(t)= (t, 4t3/2, 2t3/2) over the interval 0<t<8.

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Q: Evaluate S(-x+y+z) dx + (x+y-3) dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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Q: 1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) :…

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

Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: 4. Evaluate S. y² – 3z + 2 ds for each of the following curve C is the line segment from (1,0,4) to…

A: We have ∫Cy2-3z+2 ds C is the line segment from 1,0,4 to 2,-1,1 Now, the parametric equation of the…

Q: (i) Evaluate S(z + 5i) dz where the path is the line From z = 1 to z = 2 +i

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Q: The equation of a line perpendicular to 4x+7y– 63 =0 is Oy- z 6 Oy--- I. Oy =z+

A: See the details solution in below

Q: 1. Show that the lines 2x + 3y = 1 and 6x - 4y - 1 0 are perpendicular.

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

Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Evaluate ds, where C is the path defined by c(t) = (t², 9t, 4t³3/2) where 0 <t < 2.

A: Given integral c z^2/x ds, C(t) =(t^2, 9t, 4t^3/2)  where 0&lt;= t&lt;=2

Q: Find the distance between the skew lines r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

A: Given r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

Q: Find a distance from the point S(1,1,5) to the line x=1+t, y=3-t,and z= 2t

A: We need to find the distance of the point (1,1,5) and the given line.

Q: Compute fs(-y + ye®Y)dx + (x + xe®Y)dy, where S is the path: start at (0,0) and then go right 5…

A: Consider the provided question, According the given statement the path S is shown in the figure…

Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

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Q: Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc…

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Q: 13. Evaluate (2x + y + 3z) ds, where C is the straight line from (0, 1, 1) to (1,0, 1).

A: we have to evaluate

Q: Find Sc((x² + 3y)i + 3y³j) · dr' where C consists of the three line segments from (2, 0, 0) to (2,…

A: Given ∫x2+3yi→+3y3j→.dr→ where C consists of the three segments from (2,0,0) to (2,2,0) to (0,2,0)…

Q: Suppose that dy xy + x d.x and that the point (5,0) lies on the graph of (x, y). What is the value…

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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Q: Tind The E94ation of line which is normal to the lines X-2 = マー 3-2 %3D - and 2-X %3D 2. 3. 2.

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Q: If u=2x+y and v=x-2y then the st ream line is y2 x2 2ху+ 2 صواب ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

A: