TRUE OR FALSE? The given line integral is independant of path.

Q: integral i

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Q: (3, 1) (у? + 2ху) dx + (- 1, 2) (x² 2ху) dy +

A: We have to show that the curvilinear integral is independent of path and we have to find its…

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

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Q: What is the Fundamental Theorem of line integrals?

A: Our Aim is to define Fundamental Theorem of line integrals

Q: What does the integral dydx represent?

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Q: Show that integral - infinity  to infinity  x dx is divergent.

A: We will evaluate the limit of the integral using two different routes and see if we get the same…

Q: Use Green's Theorem to evaluate the line integral

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Q: show the line integral is independent of path

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Q: Evaluate the integral. ∫t3  et dt

A: ∫t3  et dt  We need to evaluate the integral.

Q: Using only the definition of RS-integral, evaluate 2 ,2 d[x}.

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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: Сompute 1. f dx, where f(x)=|x|.

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Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: If line Integral is path independent then there exist a function which is called potential function

Q: Use u-substitution to evaluate the integral. 3 + 5 Vx dx 3 2 + 5 Vx dx =O

A: Given query is to eveluate the integral.

Q: X' 2 -1 Vx * dx X,

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Q: In what way is Stokes’ Theorem a generalization of the Fundamental Theorem of Line Integrals?

A: Given: In what way is Stokes’ Theorem a generalization of the Fundamental Theorem of Line Integrals?

Q: Evaluate the line integral -ydx+ xdy along the curve C :y = 12x from (12, 12) to (0,0). NOTE: Enter…

A: In this question , we can find the given line integral.

Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: What is the Fundamental Theorem of line integrals? Explain how it relates to the Fundamental Theorem…

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Q: Find the integral m tanx X, 1+x?

A: Given :

Q: Using only the definition of RS-integral, evaluate 2 ,2 x* d[x}.

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: dx - Evaluate V4x' +9

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Q: Evaluate the line integral F.dr

A: In this question, we find the line integral for given vector function and parametric path.

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: (a) Solve the line integral yzdx - xzdy + xyzdz on a particle that moves along the line segment from…

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Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: Compare and contrast the Fundamental Theorem of Calculus and the Fundamental Theorem of Line…

A: compare and contrast the fundamental theorem of calculus and the fundamental theorem of line…

Q: integral t 3 et dt

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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: Show that the following line integral is path independent and evaluate its value. Show the details…

A: Solution:

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: Step:-1 Note:- 1. ∫∇F.dr =∫fx i +fy j dx i +dy j  2. Fundamental Theorem of Calculus:- ∫bc F'(x) dx…

Q: express the length of the curve as an integral but do not evaluate it. r = sin3 θ, 0≤ θ ≤ 2π

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Q: dx 1 Vx + x3

A: Answer

Q: Using only the definition of RS-integral, evaluate |x* d[x}.

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

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Q: (5)Obtain the integral curve for x 2+y = x passing through the point

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

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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: Show that the curved integral does not depend on the path joining its points and find the integral…

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Q: Using only the definition of RS-integral, evaluate x* d[x]. 0.

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Q: et dz V1-e2x

A: Given problem:-

Q: Evaluate the integral ex 2e-2x - 3e2x | Arcsin V6e2x 2 A V3 +C ®Arcsin l V3e2x +C B © 2/2e-2x - 3e2x…

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Q: Use Green's Formula to evaluate the line integral along the positively oriented closed curve C:

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Q: Using only the definition of RS-integral, evaluate x* d[x].

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Q: State the Fundamental Theorem for Line Integrals

A: To State: Fundamental Theorem for Line Integrals Here we will use the knowledge of fundamental…

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: We have  I=∫(0,0)(3,5) cosh(x23+y25)(10xdx+6ydy)apply Green's…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.