Evaluate I=∫C(sinx+9y)dx+(8x+y)dy for the nonclosed path ABCD in the figure. A=(0,0),B=(4,4),C=(4,8),D=(0,12)
Evaluate I=∫C(sinx+9y)dx+(8x+y)dy for the nonclosed path ABCD in the figure. A=(0,0),B=(4,4),C=(4,8),D=(0,12) (1 point) Evaluate I figure....
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3) 5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
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
8. Evaluate $c (4xy3 + 3y) dx + (8x – 6x?y?) dy where C is the triangle formed by vertices (0, 0), (3,0), (3, 4) oriented counterclockwise
7. Evaluate (6x - 6y+8) dx+(4 +9y +7) dy where C is the boundary of the triangle in the ry plane, wit h vertices at (0,0), (1,0)and (1,4) traversed once anticlockwise. (a) 10 (c) 20 (b)-8 (d) 8 10. Find the flux of F =-rit 2yj otward across the ellipse-+ -1. (a) 36π (b) 18m (c) o (d) 6π 7. Evaluate (6x - 6y+8) dx+(4 +9y +7) dy where C is the boundary of the triangle in the ry plane,...
Dx+Dy = e b. -D r + Dx + I + y = 0 C Dx+Dy = e b. -D r + Dx + I + y = 0 C
x dx dy + y) dx dy 0 (b (d a)(c) Answer: (a) x dx dy + y) dx dy 0 (b (d a)(c) Answer: (a)
(8 pts) c. Sc(y2 +evt)dx + (x3 + tan y2)dy, where is the path given in the figure starting from (0,0) going around the rectangle and returning to the point (0,0). (0,1) 72.1) I (0,0) (2.0)
(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).
9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the graph of y-x3 and from (1,1) to (0,0) along the graph of y x. Draw a sketch of C. Theorerm to compute ф F-ds where Fay3 dx + (x343xy?) dy and C is the path that you drew in 11a. 9. Green's Theorenm a. Green's Theorem: ap Fdx+Fzdy- b. Let C be the path from (0,0) to (1,1) along the...
Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40 Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40