Use Green's Theorem to evaluate the line integral along the given positively oriented curve. S. cos y dx + x* sin y dy, C is the rectangle with vertices (0, 0), (5, 0), (5, 2), and (0, 2)

Q: Evaluate 8(2x + y) dx + 8xy dy on the given curve from (-1, 2) to (2, 5). (-1,2) (-1,0) X (2,5)…

A:

Q: atu + 32₂ DEU + 22₂2²1 = 0 Draw the characteristic curves. U=U (2₁t) 2, t ER

A:

Q: Use Green's theorem to evaluate , (5xy + x2 + y?) dx + (x²-y)dy where C is a closed curve that is…

A:

Q: QUESTION 6 Use the Green's Theorem to evaluate the line integral xfydx +xy dy. where C is the…

A: Using the given vertices we can draw the required triangle and then apply Green's theorem to…

Q: (20 points) Evaluate the following line integral along the positively oriented curve C consisting of…

A: To find the final answer for the line integral, we need to evaluate the integral over each segment…

Q: Use Green's Theorem to evaluate Se (y? – tan-1 (r)) dr + (3r + sin (y)) dy, where C is the boundary…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 11. Let F(x, y, z) = = (), and let P represent the path that follows the from (1, 0, 1) to (0, 1,0),…

A:

Q: 7. Determine which of the following functions are differentiable at all the z-plane or some region…

A:

Q: 2. Let F(x, y, z) = (6xyz+4x) i+(3x² z+ze=v)j+(3x²y-e-") k, and let C be the portion of the…

A:

Q: Let C be the curve connecting (0,0,0) to (1,3,1) to (3,4,4) to (2,1,3) to (0,0,0) Evaluate + y)dx +…

A: Given,     and

Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

A:

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(zt) î + at j+ sin(rt) k. %3D…

A:

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

A:

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

A:

Q: Find the ccw circulation of F = around the curve C: from (0, Guam ( %3D

A:

Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: Use Green's theorem to evaluate F• dr. (Check the orientation of the curve before applying the…

A: Given Fx,y=ycosx-xysinx, xy+xcosx

Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

A:

Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

A: Given that  The equation  cos(πx)-x^2y+e^(xx)+yz=4  Point (0,1,2) To find the equation of the…