7. Using Green's Theorem evaluate following line integral: (x + y)²dx – (x² + y?)dy L Here L runs through triangle ABC in positive direction with vertices A(1,1), B(3,2),C(2,5). Check your result by comparing to direct computation of Integral.

Q: 2. Give iterated integrals for (xz*)dS where S is the part of the cylinder x² + y = 9 above the…

A: Given that x2+y2=9 and the part of the cylinder which is above XY plane implying that z > 0. We…

Q: Evaluate (₁ F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

A: NOTE: Refresh your page if you can't see any equations. . C:=smooth curve form (-5,4) to (3,2)…

Q: 4) Use a potential function to evaluate the line integral. The integral is path independent. L0=…

A: If F is a vector field defined on R  and F=∇f for some scalar function f on R, then f is the…

Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.…

A:

Q: Use the Fundamental Theorem of Line Integrals to calculate E. dr exactly. F = 6 sin(6x + y)i +…

A: Given

Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

A:

Q: Verify Stokes's Theorem by evaluating F.dr as a line integral and as a double integral. F(x, y, z)…

A:

Q: Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line…

A: By Green's Theorem, we have where R is the region enclosed by curve C.

Q: (5) Evaluate the line integral by using Green's Theorem (a) fexdx – xdy Cis the circle with center…

A: a)∫Cydx-xdy Where C is the circle center the origin and radius 8 Now we know that the parametric of…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

A:

Q: Jse Green's theorem to evaluate line integral | V8 + x3 dx + 9xy dy where C is a triangle with…

A:

Q: Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and…

A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

Q: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

A: Given line integral is ∮Cex+y2dx+ey+x2dy, where C is the boundary of the region between the parabola…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

Q: Evaluate     CF · dr using the Fundamental Theorem of Line Integrals. F(x, y) = e2xi + e2yj   C:…

A:

Q: Use Fubini's theorem to compute the double integral R f(r, y)dA where f(r, y) = 2x²y+ ry-2 and…

A:

Q: Use Green's Theorem to calculate the line integral shown in the figure, along the C curve that…

A: Given integral is ∫Cxydx+2x2dy. We have to calculate the given line integral along the C curve that…

Q: Calculate the line integral x y dx + x² y³ dy where C is the triangle with vertices (0,0), (1,0),…

A:

Q: 22. To determine [x Inx dx pick the strategy that could work. a. A rewriting of the integral to fx*…

A:

Q: Determine if Green's theorem can be used to evaluate the line integral. Then evaluate based on your…

A:

Q: Evaluate the line integral along the given paths.       C(x2 + y2) ds   a) C: line segment from (0,…

A:

Q: Q2 Use Green's theorem to evaluate the line integral [F•dš where F = 2xyi +(x- y²)j and C is the %3D…

A:

Q: Evaluate the line integral ∫AB(x+y)dx+xdy for two paths of integration: AB is the line segment from…

A: We need to find the following integral: a) AB is line segment from A(0,0) to B(1,1) b) AB is the…

Q: Consider the following line integral. xy dx + xy3 dy, C is counterclockwise around the triangle with…

A:

Q: Using Green's theorem in the plane, evaluate (x'y dy - x²y dx), where C is the triangle with…

A: As we know that; The Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydxdy Given: I=∫Cx3y2dy-x2y3dx So,…

Q: Q2 Use Green's theorem to evaluate the line integral F•ds where F = 2xyi +(x-y')j and C is the path…

A: In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a…

Q: of. F. F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

A: We need to find integral.

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

A: The Green's theorem is, ∮cPdx+Qdy=∬D∂Q∂x-∂P∂ydA On comparing with given equation, P=cosyQ=x2siny…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. S. cos…

A:

Q: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

A:

Q: Evaluate the line integral ∫CF→⋅dr→ using the Fundamental Theorem of Line Integrals if…

A:

Q: y=x² from (0,0) to (1,1). | Compute the line integral of f(x)=2x over the curve 2009

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4 y…

A:

Q: .2 Evaluate the line integral xy dx + x-dy, where C is the path going counterclockwise around the…

A: Given, ∮Cxydx+x2dy, Where C is the path going counterclockwise around the boundary of the rectangle…

Q: Use Green's Theorem to evaluate the line integral. Begin by sketching the region S. (e* + 5y) dx +…

A:

Q: compute the line integral of the function f(x,y,z) = x^2 +3y along the circle x^2 +y^2=4 from (0,0)…

A:

Q: :/F. F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify…

A:

Q: xy dx + x2y3 dy, Cis counterclockwise around the triangle with vertices (0, 0), (1, 0), Jc and (1,…

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6…

A:

Q: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

A: We will use greens theorem

Q: . Apply Green's Theorem to evaluate the given integrals: a. 2x +y)dx + (2xy = 3y)dy where Cis any…

A:

Q: 1.Evaluate the line integral ∫CF→⋅dr→ using the Fundamental Theorem of Line Integrals if…

A:

Q: Calculate the double integral. IT x 0, 3 R = 0, Зx sin(x + y) dA, R

A:

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

A: .

Q: Using Green's theorem, convert the line integral §(6y² dx + 2xdy) to a double integral, where C is…

A: Given integral, ∮C6y2dx+2xdy Here C is the boundary of the square with vertices ±2,2 and ±2,-2.…

Q: Use Fubini's theorem to compute the double integral R f(x, y)dAwhere f(x, y) = ye and R = [0,1] ×…

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A:

Q: d) Use line integral method to evaluate F(x, y)• dř ,where R 1 F(x, y) = (3x y°i + 4xy² j) and M, N,…

A: The graph of curves y=x2, y=x is as follows The yellow colored region is region R

Q: 2. Consider the triangle {(x, y)| x, y > 0, 2x + y < 1}. Let C be the boundary of this triangle…

A: Given triangle is x,y:x,y≥0,2x+y≤1. Let C be the boundary of this triangle oriented in the…

Q: that the in tegral is inde pen dent the path, and v6e S how the Fundamental to of of Line Integrals…

A: