A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by curves (y=x?), (x=y?) by using the of Green's %3D Theorem.

Q: Evaluate the line integral, where C is the given curve. xy dx + (x − y) dy, where C consists of…

A: In the above line integral there are two segments which needto be seperated. First (0,0) to (1,0) so…

Q: Given The boundary of C: 0 ≤ x ≤ π,0 ≤ y ≤ sinx With Green's Theorem, Evaluate this line integral. $…

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Q: Use Green's Theorem to evaluate the line integral. y? dx + xy dy C: boundary of the region lying…

A: From Green's theorem, ∫CMdx+Ndy=∬∂N∂x-∂M∂ydydx If M=y2 ;N=xy, then ∂N∂x=y ; ∂M∂y=2y

Q: Find the value of the line integral  ∮ C (2*y + e^x) dx + (ln(y) + 8*x) dy, where C is a closed path…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. The Green's theorem…

Q: Evaluate the line integral of f(x,y) along the curve C. f(x, y) = y + x, C: x2+ y2 = 1 in the first…

A: Line integral

Q: Calculate the integral xy² dy – x²y dx where L is along the curve x + y ² = a? (a > 0) in a…

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Q: Calculate the double integral || x + y)?e -r dx dy where R is the square with vertices (4, 0), (0,…

A: Given: ∫∫Rx+y2ex2-y2 dx dy where R is the square with vertices 4,0, 0,4, -4,0, 0,-4

Q: Sketch in the xy-plane the region of integration for the integral /6 (cos 20 g(r, 0)r dr de. w/6…

A: Given Data The integral is ꭍ-π/6 π/6 ꭍ1/2 cos 2θ g(r,θ)rdrdθ.   The sketch of the region of…

Q: Verify Green's Theorem by evaluating both integrals ƏM ? dx + x² dy dA ax ду for the given path. C:…

A: Given : ∫c y2 dx + x2 dy , Where, c : boundary of the region lying between the graphs of y =x &…

Q: Calculate the integral (x – y) dx + (x + y) dy I = x2 + y2 where L is along the curve y = cos x,…

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

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Q: O (y²-x² ) dx+ (x² +y?)dy be the line integral on the boundary of the region enclosed by Let y=0, x…

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Q: #6. Evaluate the line integral (y dx +z dy +x dz), where C is given by x = Vt, y = t, z = t? with…

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

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Q: Verify Green's Theorem by evaluating both integrals dA dx + x2 dy ax for the given path. C: boundary…

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Q: Use Green's Theorem to evaluate the line integral. | y? dx + xy dy C: boundary of the region lying…

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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: Use Green's Theorem to evaluate the line integral. | y2 dx + xy dy C: boundary of the region lying…

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Q: Verify Green's Theorem by evaluating both integrals ƏN y2 dx + x² dy dA ay for the given path. C:…

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Q: Evaluate the iterated integral. V9-y y dx dy V9-y y dx dy = i

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Q: Evaluate the line integral (xy dx + y dy), where C is the curve y = sin(x), 0 ≤ x ≤ π/2

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

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Q: Evaluate the line integral ex dx - xy dy +y dz, where c(t) = (1, t, t ), 0 sts 1. %3D

A: As per our guideline we are supposed to answer only first asked question.Kindly repost other…

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 double integral I = | | (2 – cos(x + y)) dA D when D is the bounded region enclosed by…

A: Given- I=∬D2-cosx+ydA, where D is the region bounded by the lines x+y=π,x=0 and y=0 To find- The…

Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Final answer is 65/84.

Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy = dA ду ax for the given path. C:…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

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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: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

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Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

Q: 1+y dy

A: We can solve the given integral as follows:

Q: Evaluate the line integral I of the one-form w = (y + z) dx + (x + 2) dy + 10z dz over the line…

A: Given: One-form ω=y+zdx+x+zdy+10zdz and the line segment joining 0, 0, 0 and (3, 1, 0). To find:…

Q: Verify Green's Theorem by evaluating both integrals |y? dx + x2 dy dA ax ду for the given path. C:…

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Q: Evaluate the line integral Ja? + xy)dx + (x - y²)dy where C is the positively oriented boundary of…

A: we need to calculate the given line integral about C where C is the boundary of the region bounded…

Q: Calculate the integral of C being the curve given below. y= 3+x y= 3-x 6x dS C

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Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

Q: Calculate the line integral ∫Cyxdx+dy over the curve y=lnx in the interval 1≤x≤e (Figure 4).

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Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y² dz, C is the line segment…

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Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t3, t2) for 0 <t< 3

A: Here, x=2+t-1 y=t3 z=t2

Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t³, t2) for 0 <ts 3

A: Given: From the above function, the following can be written,

Q: Evaluate the line integral, where C is the given curve. z? dx + x2 dy + y² dz, C is the line segment…

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Q: Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's theorem…

A: .

Q: Evaluate the given circulation integral on the closed curve C below. $ (x² + y²) dx – 2æydy (1, 1) y…

A: From the given problem:   I=∫cx2+y2dx-2xydy   Fro the Stoke's theorem:   ∮F→.dr→=∬curlF→n^ds   It…

Q: Evaluate the triple integral. SITE3*y dV, where E lies under the plane = 1+x + y and above the…

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Q: Evaluate the line integral, where C is the given curve ʃc (x+9y)dx +x2dy, where C consists of line…

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Q: The double integral f(x)g(y)dydx ,where a,b.c, and C d are constants, is equal to

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Q: Use Green's Theorem to evaluate the line integral. v? dx + xy dy C: boundary of the region lying…

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