Use the Fundamental Theorem of Line Integrals to evaluate the following. S(ze" +1, xe" ). dr such that 7 (t) = (t +3, t+1, 2-t) and 0st52.

Q: Evaluate the iterated integral. 4z (In(x) xe- dy dx dz J3

A: Formulae used∫e-ydy = -e-y + C∫x2dx    = x33 + C ---------------------------------------- I…

Q: S,(4y³ +-) dy y3.

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Q: Express the iterated integral in the opposite order. dy dx

A: First option is the correct option. Find the region of the integration graphically. The value for y…

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: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. + dy

A: Line integral

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy…

A: Gievn, x=4t,y=8t And 0≤t≤1

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

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Q: In y dy dx 1 xy 20.

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Q: Evaluate the line integral, where C is the given curve. | (x/y) ds, C: x = t3, y = t4, 1sts 2

A: Given: I=∫C(xy)dsC: x=t3  and  y=t40≤t≤2

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤t≤ 1. √(x + 3y²) dy…

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Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 <ts 1. / (x+ 3y²) dy #4

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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: Give an approximation of the following integrals using Composite Trapezoidal rule: a) os- cos(x) dr…

A: Trapezoidal rule ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2​)+2f(x3​)+⋯+2f(xn−2​)+2f(xn−1​)+f(xn​)) where…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

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Q: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

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

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

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Q: Set up the integral to find the length of the curve f(x) = V1 – 2? for 1/v2 <x < 1.

A: Please see the answer below.

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: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dy

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We can solve this as follows:

Q: Find the integral of r(t) = (3t2 + 4t, 2, e') from 0 to 1.

A: Consider the following vector: rt=3t2+4ti^+2j^+etk^ Integrate the above vector:…

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 st< 1. + 3у?) dy

A: We need to evaluate the following line integral ∫Cx+3y2dy Where, C is defined as x = 4t, y = 8t ;…

Q: Use the Fundamental Theorem of Line Integrals to calculate F.dr exactly. F = (x + 2) í + (2y + 3)j…

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Q: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

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Q: Evaluate the line integral by the two following methods. dx + x2 dy Cis counterclockwise around the…

A: The solution is given in the next steps.

Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Evaluate the line integral, where C is the given curve. (x + 9y) dx + x² dy, C consists of line…

A: To evaluate the line integral, consider the curveC1 consisting of the line segment from0,0to9,1. The…

Q: Evaluate the iterated integral f Só 6x²y° dxdy

A: Given:    ∫03∫02 6x2y3 dxdy

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dx + 5x2y2 dy

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. + 3у?) dy

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Q: Show that for c =5 that PV sin r dr + PV | sin(x+c) dr. This shows us that when the improper…

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Q: Estimate the following definite integrals using the trapezium rule with six strips: 0.6 (a) Vx3 +1…

A: As per the company guidelines we are supposed to solve first 3 subparts of a question. Kindly post…

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 integral 16–z² x? dz dy dx x²+y²

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Q: 3(e). If it is true that the line integral F. dr 0 for all closed curves C₁ show that the line…

A: Given: 3C.For all closed curves C, line integral ∮CF.dr=0 and line intergral over a non-closed curve…

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

A: We will calculate the given line integral utilizing given information.

Q: Evaluate the line integral by the two following methods. dx + x2 Cis counterclockwise around the…

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Q: 1+y dy

A: We can solve the given integral as follows:

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: If ƒ is continuous and f(t) dt = 16, find the integral

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1.

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Q: V 11y2 – 15 dy y2

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1. 3у?) dy

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Q: Evaluate the line integral IF.då over the path C to Q (2,4) from P(0,) where F(xy) = 2xy2 + 3y f 131…

A: According to question, Given function, F→x, y = 2xy2 i^ +3y j^,We have to calculate line integral…

Q: Q2. Evaluate the iterated integral by changing the order to dx dy. eu dy dx

A: For reversing the integration order, we will replace the limit of x and y with interchangeably. Then…

Q: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…

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

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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) dy

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