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

Q: Calculate this integral a Sat-x? 3/2 x²+y²)¯ dy dx -a

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Q: Evaluate the iterated integral. 4 cos (x + y + z) dz dx dy /o Jo

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Q: If F = (x + y, x² - y) a= y = √, calculate fr F.Tds by using computing the line integral directly.)

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Q: Calculate the iterated integral. r5 CT/2 (y + y2 cos(x)) dx dy -5Jo 120

A: Given query is to find the value of the individual integral.

Q: Calculate the iterated integral. (x + y)? dx dy

A: The given integral is

Q: Evaluate the line integral along the given path. ²+ y? +z?) ds C: r(t) = sin(t)i + cos(t)j + 2k Osts

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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) =…

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Q: 6. Evaluate the line integral (x? + y² )dx – x dy along the curve C: x? + y² =' counterclockwise…

A: Given: ∫c x2+y2 dx- x dy  We have to Evaluate the given line integral along the curve C: x2+y2=1…

Q: Calculate the line integral of h (x, y)= (2n) i+(x - 2y) j; over r (1) = cos u i+ sin u j, u e…

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Q: The line integral g-dr where g= (2ry - y³)i + (a² – 2ry)j and r(t) = cos ti + sin tj,0<t<a has a…

A: Use green theorem.

Q: Evaluate the line integral along the curve C. 3xy ds; C is the quarter circle r(t) = (cos t, sin t)…

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Q: Evaluate the line integral (-3x+y)dx + (x + 3y)dy, where C lies along the x-axis from x = 0 to x = 6

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Q: Evaluate the line integral along the curve C. (xz + y) ds, C is the curve r(t) = (-4 - t) i + 2t j -…

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Q: Calculate the line integral of h (x, y) = (2xy) i+ (x² – 2ry) j; over r (1u1) = cos u i+ sin u j, u…

A: Here,hx,y=2xy i + x2-2xy jr(u)=cosu i+sinu j

Q: Evaluate the triple integral S" S, sin y² dz dy dx.

A: We need to find the triple integral ∫03∫0π∫0ysiny2dzdydx. So,…

Q: Evaluate the line integral along the given path. I ( 2+ y2 + z² ) ds C: r(t) = sin(t)i + cos(t)j +…

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Q: Evaluate the line integral by the two following methods. dx + x?y3 dy C is counterclockwise around…

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Q: Let o (x +e*siny) dx + (x +e* cos y)dy be the line integral on the boundary of the triangle enclosed…

A: We will find out the required value.

Q: Find the line integral of ƒ(x, y) = x - y + 3 along the curver(t) = (cos t)i + (sin t)j, 0 &lt;_ t…

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Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: ω=xydx+12ydy To find: I=∫αω  where α:[0,ln2]→ℝ2 with α(t)=(e2t,e-2t) ∴x=e2t,y=e-2t Now,…

Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: Evaluate the iterated integral. /2 x. 4 cos (x + y + z) dz dx dy

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Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

Q: (a) (x2 + y?) dx dy J2

A: To calculate the integral: ∫-11∫24x2+y2dx dy Solution: When we will integrate with respect to one…

Q: Evaluate the iterated integral. Tt/4 y cos(x) dy dx

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Q: Evaluate the line integral along the given path. ds [ (x² + x² +2²) 0₂ C: r(t) = sin(t)i + cos(t)j +…

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Q: Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

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Q: Evaluate the iterated integral. * T/4 y cos(x) dy dx

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Q: Let p (x +e*siny) dx + (x +e* cos y)dy be the line integral on the boundary of the triangle enclosed…

A: To find the equivalent double integral we will use the Green's Theorem also we will draw the…

Q: Compute the integral COS I dx (x + a)2 + B2 where a E R and B> 0.

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Q: 1/ Math

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Q: Evaluate the iterated integral cos (x + y + z) dz dx dy. Answer:

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Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: evaluate the iterated integral.

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Q: Evaluate the line integral along the given path. (x² + y² + z?) ds C: r(t) = sin(t)i + cos(t)j + 5k…

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Q: Question attached thanks!

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Q: Evaluate the iterated integral. TT- 9x 3x2 sin(y) dy dz dx

A: The objective is to evaluate the iterated integral.

Q: Use Green's theorem to evaluate the line integral I of the one-form W = + æ sin? (y)) dæ + (x²…

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Q: Calculate the iterated integral. 5xyV x? + y? dy dx

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Q: Calculate the line integral of h (x, y) = (2xy) i + (x– 2ry) j; over r (u) = cos u i+ sin u j, u E…

A: Given function is  hx,y=2xyi+x2−2xyj To compute the line integral over ru=cosui+sinuj from 0 to 2?.

Q: /2 TT Sin (x ty) dy dx 0

A: Consider ∫0π2∫0π2sin(x+y)dydx = ∫0π2∫0π2sin(x)cos(y)+cos(x)sin(y)dy dx =…

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.

Q: Evaluate the line integral along the curve C. y² ds, C is the curve r(t) = | 9 sin x + z2 i+ + 5tk,…

A: To find the line integral along with curve C, use the formula,…

Q: Evaluate the line integral along the curve C. x² +y² ds, C is the curve r(t) = (2 sin 6t)i + (2 cos…

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

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Q: Consider the following line integral. xy dx + x?y dy, Cis counterclockwise around the triangle with…

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Q: evaluate the iterated integral.

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Q: Calculate the iterated integral

A: The given double integral is  I=∫01∫04xy+ydx

Q: Use Green's Theorem to evaluate the line integral. e cos(2y) dx - 2e* sin(2y) dy C: x2 + y? = a?

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Q: Evaluate the integral: L x2 + y² dy dx by using polar coordinates.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.