Evaluate the line integral along the given path. I ( 2+ y2 + z² ) ds C: r(t) = sin(t)i + cos(t)j + 5k Osts 9

Q: Evaluate the line integral along the given path: 1. So ry ds, where C : r(t) = 4ti + 3t²j, 0 < t <…

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Q: find the line integrals along the given path C. ∫C (x - y) dx, where C: x = t, y = 2t + 1, for 0≤ t≤…

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Q: Evaluate the line integral , F. dr where F = (-4 sin x, –3 cos y, 10xz) and C i: the path given by…

A: Given that F→=-4sinx, -3cosy, 10xz and C is the path given by r→t=2t3, t2, -2t for 0≤t≤1 We have to…

Q: Evaluate the line integral Ĥ. dř where Ĥ = e" î + [xe" + In(2)] ĵ + º Â and the curve C is defined…

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Q: Evaluate the iterated integral below. π T/4 A lago S. 0 1 y cos (x) dy dx

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Q: Evaluate the line integral along the given path. S ² + y² + 2²) ds C: r(t) = sin(t)i + cos(t)j + 7k…

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Q: Evaluate the line integral, where C is the given curve. [x² x sin(y) ds, C is the line segment from…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) a…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

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Q: :+cos(x2) dz. =(s* + 1) 4.1 with C: |z- il -. 4.2

A: Explanation of the answer is as follows

Q: Consider: dr, C: r(t) = (t, t²), te[0,1] Which one of the following "regular" integrals represents…

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Q: Q.4 Show that in the following problems, the line integrals are independent of path of integration…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. √(²x- (y - x)…

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Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: Find the line integral of ƒ(x, y) = x - y + 3 along the curver(t) = (cos t)i + (sin t)j, 0 &lt;_ t…

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Q: Evaluate the integral t 8e* sin(t – s) ds 0.

A: The integration can be done using by-parts. The order of preference is given by ILATE rule. Hence…

Q: tan x dy S dx S 1+y?

A: Explanation of the answer is as follows

Q: Evaluate the line integral along the given path. C: r(t) = sin(t)i + cos(t)j + 3k osts 8

A: The given line integral is ∫Cx2+y2+z2 ds where c is a curve rt=sinti+costj+3k  and  0≤t≤π8.…

Q: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 1 from…

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Q: Evaluate the line integral along the given path. ds [ (x² + x² +2²) 0₂ C: r(t) = sin(t)i + cos(t)j +…

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Q: Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

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Q: Find the line integral of F =9xy*ï +(x² + 3),yj over the path L.

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Q: What is the value of the line integral on the field 5xy? 5æ?y F(x, 3) = ()i+ ( 2 along any path from…

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Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

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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: Evaluate the iterated integral. * T/4 y cos(x) dy dx

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Q: Evaluate the iterated integral. 21 V441-y у dx dy

A: NOTE: Refresh your page if you can't see any equations. . ..............(1)

Q: Find the line integral along the given path C. [(x - y)dx, where C: x=t, y = 3t+8, for 0 ≤t≤6 с √(x…

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Q: Use the direct method to evaluate the path integral for the work done by F(x, y) = (y, -x) along…

A: -4π

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √((x-x) (y -…

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Q: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 4 from…

A: Given  ∫C(-y,x-y).dR→ where C is upper part of circle  x2+y2=4 from (-2,0) to (2,0).   Note-As per…

Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: Q21 Verify Green's theorem for $. (xy² + x²)dx + (4x – 1)dy where Cis shown in the figure by (a)…

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Q: Evaluate the line integral along the given path. (x² + y² + z?) ds C: r(t) = sin(t)i + cos(t)j + 5k…

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Q: Evaluate the line integralſ (x + 2y) dx + x² dy, where C consists of line segments from (0,0) to (2,…

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Q: Find the integral of (t^2 sin(t)cos(t) + t sin^2 (t) )dt

A: We have I=∫t2sin2t+t2costsintdt

Q: Evaluate the line integral along the curve C. |(x+3y)dx+(x- y)dy, C: x= 2cost, y = 4sint, 0sts 4…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the integral S (* In ti+ 3t sin (t*) j+ k) dt. x(*+1)

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Q: over the graph y = e*, 0 < x < 1. Compute the path integral of f(x, y) = 2y² %D

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Q: Evaluate the line integral along the curve C. S-s - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O…

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Q: The result of the integral in 0 given |V y²– 25 -dy is 5 tane – 50 +C, y (A) True (B) False

A: To solve the following integral

Q: T/2 T/2 (b) sin(x + y) dy dx

A: Consider the given integral, ∫0π2∫0π2sinx+ydydx first, integrate with respect to dy,…

Q: Evaluate line integral F. dr, where F(x, y) =(2xy)i + (x²+3)j, and C is the path given by r(t) = t =…

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Q: b) Evaluate the iterated integral In z x e' dy dz dx 3 cx2 1 x,

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Q: Evaluate the line integral, where C is the given curve. x sin(y) ds, C is the line segment from (0,…

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