1. Let F(x, y) = (-y,x). Let C be the boundary of the triangle with vertices (0,0), (1,0), (0,1), traversed counter-clockwise. Calculate the line integral of F(x, y) over C. No Green's Theorem!
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Solved in 3 steps with 3 images
- Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)1.Evaluate the line integral ∫CF→⋅dr→ using the Fundamental Theorem of Line Integrals if F→(x,y)=(10x+10y)i→+(10x+10y)j→and Cis the smooth curve from (−1,1)to (8,9). Enter the exact answer. ∫CF→⋅dr→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) to (-2,0)
- Evaluate the line integral where F=√(1+x3) i + 2xy j and C is given by triangle with vertices (0, 0) (1, 0) , (1, 3) with counterclockwise orientation.Compute the line integral of f(x)=2x over the curve y=x^2 from (0,0) to (1,1)Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx + 4x2y dy C is the triangle with vertices (0, 0), (3, 3), and (3, 6)
- Evaluate the work line and flux line integrals of ⃗F = y^3 ⃗i + (x^3 + 3xy^2)⃗j alongthe curve y = x^3 from (0,0) to (1,1) and then along the curve y = x from (1,1) to (0,0).Let the curve C be the line segment from (0, 0) to (3, 1). Let F = ⟨2x-y, 4y-x⟩ Calculate the integral ∫c F· dr = ∫c (2x-y)dx + (4y-x)dy in two different ways:(a) Parameterize the curve C and compute the integral directly. (b) Use the Fundamental Theorem of Line Integrals.Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant
- What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the path from A(0,2) to B(4,6)?with the integral of the image where R is the triangle with vertices (0,0), (−π, π) and (π, π).1. If u = x - y & v = x + y, then the limits of integration for the integral of the change of variables are 0≤ u ≤ 2π & 0 ≤ u ≤ 2π - u 2. The Jacobian of the transformation is equal to 1/2 Which are right or wrong