Find the value of "k" for which the line integral 1+ky? 1+ kx? dy taken č [a+ xy)? (1+xy)? (1+ xy)? along a curve C depends only on the coordinates of the endpoints of C. For this value of "k" evaluate the integral between (0,0) and (1,1).

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A: Topic - length of curve using integrals

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Q: Consider the integral 3 4х f (x, y) dy dx 0, Evaluate the integral for f (x, y) = 5x²y

A: Given Data: Integrand: ∫03∫04xfx, ydydx Function: fx, y=5x2y3 Integrate the function. ∫03∫04xfx,…

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Q: 22 Calculate the value of the integral over the following C curves, a) C:/2+1| = 1 1. %3D %3D 4) e!…

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Q: Given F = &lt; x^2y, x &gt; and c is the line from P1 (2,1) to P2 (0,0) Find the integral of F • dr

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A: corresponding limit after changing the order of integration  here y = z so only this limit is change…

Q: Find the line integral along the given path C. f(x - y)dx, where C: x=t, y = 5t+7, for 0 st≤5 C √(x…

A: Topic:- application of integration

Q: 14. dy, where C: x = t, y = t², for 1 <t<2

A: Here, to evaluate: ∫Cxydy=∫12tt2(2t dt)=2∫12dt

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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: 21. Find the line integral of f(x, y) = ye along the curve r(t) = 4ti – 3tj, –1 < t < 2.

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A: Use derivative for finding the line integral.

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A: Use parametric to integration

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Q: Find the integral f(r, 0) = 4r², where 1 <r< 3, -T < e <n of

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Q: 14. Find the line integral of f(x, y, z) = V3/(x² + y² + z?) over the curve r(t) = ti + tj + tk, 1 <…

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Q: Evaluate the line integral of f(x,y) along the curve C. f(x,y)=x +y, C. y= - 2x + 4, 0<x<3 O A. 21 О…

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Q: (1,0) (1,0) | (x2 – y²) dx – 2x y dy + i | 2x y dx + (x² – y²) dy (0,1) (0,1) Calculate the above…

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Q: Consider the function y (x) = 1 + ex / 2, from the point (0,2) to (4, e2). Set up the integral that…

A: Given that: y(x)=1+ex/2

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Q: Evaluate the line integral , F. dr where F = (3 sin x, -5 cos y, xz) and C is the path given by r(t)…

A: To determine the value of the integral.

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Q: Evaluate the integral   ∫∫R sin(x2 + y2)dA,   where R={(x, y)|-1√(1-y2 )≤ x ≤ 0, -1 ≤ y ≤ 1}

A: Evaluate the integral∫∫Rsinx2+y2dAwhere R=x,y/-1-y2≤x≤0 and -1≤y≤1

Q: Find the line integral along the given path C. - y)dx, where C: x=t, y = 3t + 8, for 0 sts2 = xp(K -

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

A: We need to find integral value.

Q: Find the line integral of F(x, y, z) = x'i + yj+ zk along the line segment C from the origin to the…

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