Q6. Determine whether F (x, y) is conservat integral F dr, given that; F(x,y,z) = (1+ xy)e*y i + x²e*Y j %3D and C: 7(t) = cost i – 2sint j, 0

Q: Compute the line integral of the scalar function f(x, y) = /1+9xy over the curve y = x³ for 0 < x <…

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Q: (x² + yz), sin J nyt, (ayl +(0,0) + Cxnyl flxiy) = (w.y) = (a,0) for function fx lo,0) = ?, - ? fy…

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Q: 2xe-Ydx + (2y – x²e¬Y)dy, C is any path from (1, 0) to (3, 1) (x, y) = Evaluate the integral. Need…

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Q: Use the Fundamental Theorem of Line Integrals to evaluate F. dR where x 1 (−2x + 1)²³ y +1 and C is…

A: Given: F→x,y=lny+1-1-2x+12, xy+1+1y2+1 C is the portion of the parabola y=-x2+1 from 1,0 to 0,1.…

Q: x=3 Qs. A: Find * x²dx by using Riemann integral.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Q5:: Calculate the curve integral below. Sc (x2 + y2 + z?)ds, ve 0sts C:r(t) = sinti + costj + 2k

A: We have to evaluate the curve line integral.

Q: Evaluate the line integral C: y² = 24x from (24, 24) to (0,0). NOTE: Enter the exact answer. - gtxảy…

A: Figure of curve and direction:  Given parabola:  y2=24x That is,  y2=4*6*x One Parametrization is…

Q: Let (x, y) E R × R. Consider the following functions from R? to R? r(х, у)) %3D (-у, х) and s(x, y))…

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Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: Compute the line integral of the scalar function f(x, y) = √√/1 + 9xy over the curve y = x³ for 0 ≤…

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Q: A. Find and classify all the local maximum and minimum of the function: F(x,y) = (3x + 4x?) (y² +…

A: AS per the guidelines I am allowed to do the 1st question only. Kindly repost the other question…

Q: F(x, y, z) = (2xe*) i+ (2y + 3y?22)j+ (x²e* + 2y³z) k is conservative. Find a functionf such that F…

A: To find the function f  And then evaluate the line integral along the given curve.

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: Compute the line integral of the scalar function f(x, y) = /1+ 9ry over the curve y = x° for 0 <¤ <…

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Q: Evaluate the line integral ds along the curve C given by 7()=(2 sint, 2 cost), 0sts T.

A: Given line integral is ∫Cx+12yds. Curve is r⇀t=2sint,2cost,0≤t≤π. xt=2sint,yt=2cost Compute the…

Q: Consider: S (x?, v>dr, C: r(t) = (sint, cost), te[0,1] Which one of the following "regular"…

A: Given ∫Cx2,ydr and C:rt=sint, cost i.e. xt=sintyt=cost

Q: Calculate the integral of ƒ(x, y, z) = 2x² + 2y² + zº over the curve c(t) = (cos t, sin t, t) for 0…

A: To find line integral over the parametric curves

Q: [f.dr, where W and f = (x² + y 1V

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Q: Determines a e R so that F- dr = -2 – 4 Where F(x,y) = ay, 2 e C is the part of the circumference…

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Q: (a) Verify Green's theorem for the line integral f(x−y)dx + (x+y)dy, where C C is the unit square…

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Q: Consider the following functions. F(x, y, z) xi - zj + yk r(t) = 4ti + 9tj - t²k 16² F. dr, where C…

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Q: Find the line integral where C is the semicircle y = A. I = 96 B. I-160 80 162 traversed from (4,0)…

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Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: c. Find approximation of the value cos(65") with error less than 5 x 10-5.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.