use the Fundamental Theorem of line Integrals to evaluate F. dR, where F (*.y) = < y. - X and C is the line segment from (1.') to (25, 1).

Q: Evaluate the integral: ² ls teu du ds dt 0

A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where U + dy

A: Given

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

A: Line integral

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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: Express the limit as a definite integral on the given int lim [2(xf)3 – 7x*]Ax, [2, 8] i = 1 dx J2

A: We have to solve

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: Use double integral to find the average temperature of T(x. y) = 10-8r -2y

A: Temperature function is given as - Tx, y = 10-8x2-2y2Average temperature = ∬10-8x2-2y2dxdyGiven…

Q: What change of variables is suggested by an integral containing Vx? + 36?

A: For, an integral containing  x2+36 we can change variable by substituting, x=6tanθ, As it will get…

Q: express the length of the curve as an integral but do not evaluate it. r = eθ + 1, 0 ≤ θ ≤ π/2.

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

A:

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: Use Green's theorem to determine the value of the integral where the curve x2 + 4 = 1 traveled…

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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: Set up the integral to find the length of J (X) = e from x = You don't have to integrate it. 0 to x…

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Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Set up an integral that represents the arc length of the function y = 4x4 + 5x from the point (0,0)…

A: We have to find a, b and f(x)

Q: Set up an integral that represents the arc length of the function y = 4a4 + 5x from the point (0,0)…

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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: Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Trapezoidal Rule with h=0.05.

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Q: Use a table of integrals to find the length of the curve y = x² from x = 0 to x = 2. %3D

A: The equation of the curve is given as, y = x2 we need to find the length of curve in the interval x…

Q: line

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Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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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 = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

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, where Cis the given curve. xyz? ds, C is the line segment from (-1, 4,…

A:

Q: Evaluate the line integral of the function p(x.y)=y-x,over the straight line Joining the two points…

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Q: dx 1 Vx + x3

A: Answer

Q: Set up an integral that represents the length of the curve. X = Vу - 9у, 1 s y <4

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Q: 8r dr. 4. Evaluate the improper integral or show that it diverges:

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Q: Set up a definite integral to find the length of the curve  y= (3/4)x(4/3) - (3/8)x(2/3) over the…

A: The given curve is,

Q: 1. Estimate the integral using Trapezoidal approximation rule with n=4: 2 + t)dt

A:

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

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

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: f(x)=sin(x)/x_between 0 and 1 using Trapezoidal

A: fx=sinxx Trapezoidal rule fx≈h2fa+2fa+h+fa+2h+---+fb a=0, h=0.05 and b=1

Q: Find the c that satisfies the MVT for Integrals. f(x) = x² [0,4]. over

A: Given: f(x)=x2,  [0,4]

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

A:

Q: 3. Reverse the order of integration in 24e² dydx and then evaluate the integral with the new limits

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

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Q: 2. Estimate the integral using Simpson's approximation rule with n=4: sin t dt

A: To estimate:∫0πsint dtn=4

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

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Q: b) Calculate the line integral of F along the boundary of the rectangle [0, 1 x[-1, 2], traversed…

A: According to the given information, consider the vector field. It is required to calculate the line…

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A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Evaluate the line integral 11y dy over y = x for 0 < x < 3. (Use symbolic notation and fractions…

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Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

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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

A: