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.
Show that the line integral is independent of path by finding a function f such that...
(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).
(4,9,-5) Evaluate the integral | ydx+x dy +7 dz by finding parametric equations for the line segment from (3,2,2) to (4,9. – 5) and evaluating the line integral of F=yi + xj + 7k along the segment. Since F is conservative, the integral is independent of the path. (3.2.2) (4.9.-5) | ydx + x dy+7 dz=0 (3.2.2)
path in R2. And use potential function to Problem 6. Show that line integral is independent evaluate integral :2xydx +(x2- 1)dy, where C runs from (1,0) to (3,1) on path in R2. And use potential function to Problem 6. Show that line integral is independent evaluate integral :2xydx +(x2- 1)dy, where C runs from (1,0) to (3,1) on
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
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
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
The path integral of a function f(x, y) along a path e in the xy-plane with respect to a parameter r is given by 2. fex,y)ds= f(x),ye) /x(mF +y(t" dr , where a sr sb. (a) Show that the path integral of f(x, y) along a path c(0) in polar coordinates where r=r(0), α<θ<β, is Sf(r cos 0,rsin e) oN+( de. (b) Use this formula to compute the arc length of the path r 1+cos0, 0<0 27 The path integral...
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 _______
Calculate the work done by the force F= (x-2y)i+(x+y)j in a) 2. moving from point A at (0,2) to point B at (2,18) along the path y 4x2+2. [5 marks] - Evaluate the line integral(xdy+ydx) along a path C that is b) [5 marks] to t described by x= cos(f), y=2sin(t)+5, from t =: 2 Calculate the work done by the force F= (x-2y)i+(x+y)j in a) 2. moving from point A at (0,2) to point B at (2,18) along the...
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...