Evaluate the integral 3,3 + 2 where C is the positively oriented circle 2-22
Evaluate line integral ( F. dr where C is any positively oriented simple closed curve that encloses the origin by using a circle of radius r, and r is small enough so that the circle lies entirely inside C given F(x, y) = ? 1)_ 2xyi +(y2 – xº)j Ans (x² + y²)
5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify
5. Compute the integrals 23 dz e2 22-9)' where C is the (positively oriented) circle with equation |z|-1. Justify
10. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C in the xy-plane. $ 5xydx +4xdy , where C is the triangle with vertices (0,0), (5,4), and (0, 4).
(5 points.) Let C be the positively oriented circle of radius 2 around the origin. The mapping w 1/(2(22-1(22-9)) transforms C into a closed curve I. Find the winding number of 1.
(5 points.) Let C be the positively oriented circle of radius 2 around the origin. The mapping w 1/(2(22-1(22-9)) transforms C into a closed curve I. Find the winding number of 1.
Use Green's Theorem to evaluate the line integral along the given positively oriented curve I = Sc (2y + 7eV*)dx + (3x + cos(y2))dy, where the curve C is the boundary of the region enclosed by the parabolas y = 9x2 and x = y2
could u please solve them all Thanks :)
(15 points) Evaluate the given integral along positively oriented curve 2 and y2 where C is the boundary of the region enclosed by the parabolas y # (Hint: Use Green Theorem). (15 points) Let F = (6fpi + (2x3jj + .k be given. (a) Evaluate f F-dr along the plane curve y = 12 fronn (0.0.0) to (2,4,0). b) Evaluate, curl(F), div(F) and div(curl(F))
(15 points) Evaluate the given integral along positively...
We say that zois a source or a sink for a given flow f(2) if there exists a circle around it such that the contour integral of f(z) around this positively oriented circle is purely imaginary with imaginary part positive or respectively negative. Alternatively, we say that zois a positive or negative vortex for a given flow if there exists a circle around it such that the contour integral of f(z) around this positively oriented circle is real positive or...
3. *(7 pts) Find the positively oriented simple closed curve C for which the value of the line integral is the maximum, where C is piecewise smooth.
3. *(7 pts) Find the positively oriented simple closed curve C for which the value of the line integral is the maximum, where C is piecewise smooth.
2. (3 pts.) Let C denote the unit circle, oriented clockwise. Evaluate the line integral ydx dy in two different ways: first by parameterizing the curve and using the definition of line integral; then, use Green's theorem.
2. (3 pts.) Let C denote the unit circle, oriented clockwise. Evaluate the line integral ydx dy in two different ways: first by parameterizing the curve and using the definition of line integral; then, use Green's theorem.
Use Green's Theorem to evaluate the line integral ſc 543 dx – 5x3 dywhere C is the positively oriented circle 22 + y2 = 16. Enter the integral including limits of integration that you find after applying Green's Theorem. Also, enter the value you find after evaluating the integral.