
path in R2. And use potential function to Problem 6. Show that line integral is independent...
4) Use a potential function to evaluate the line integral. The integral is path independent. S. (2xy2 + y®)dx + (x^2 +2y2 + 2xy) dy+(x2y + yº) da, y(t) = (1+0,7%, (1 - 2)e'), 05152
Show that the line integral is independent of path by finding a function f such that ∇f = F. C 2xe−ydx + (2y − x2e−y)dy, C is any path from (1, 0) to (4, 1) f(x, y) = Evaluate the integral.
(1 point) Show that the line integral 2xe-y dx + (4y – xey) dy is independent of path 0Q - M Evaluate the integral ( 2xe”) dx +(4y= xe=") dy = where C is any path from (1,0) to (3, 1).
4.Use Green's Theorem to evaluate the line integral. ∫C 2xydx + (x + y)dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x2_______ 5.Use Green's Theorem to evaluate the line integral. ∫C ex cos(2y) dx - 2ex sin(2y) dy C: x2 + y2 = a2 _______
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and y-x2 oriented in the positive direction
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...
Question 22 1 pts Compute the path integral of F = (y,x) along the line segment starting at (1,0) and ending at (3,1).
Evaluate the function of the line integral where ? is given by ?=11cos ?, ?=11??? ? in an interval of
x2-y2dk,x-y)dy, and (x-yds 0t2
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C from (0,0) to (3,0), the path C2 from (3,0) to (2,1), and the path C3 from (2,1) to (0,0) by applying the following steps. (a) Evaluate (x + 2y) dx + c'dy, by parametrizing C C (b) Evaluate [ (x + 2y)dx + x>dy, by parametrizing C, (c) Evaluate | (x + 2y)dx + x’dy, by parametrizing C3 (d) Evaluate (+2y)dx + xºdy