(10 pt) Evaluate rydx + x?y dy where is the triangle with vertices (0,0), (1,0),(1, 2)...
4. Evaluate (2 + y)dA, where D is the triangle with vertices (0,0), (0,1),(1,0).
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where C is the triangle with vertices (0,0), (1,0) y (1,2)
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...
(10 pts) Evaluate where C is the boundary of the square with vertices (0,0), (1,0),(0,1) and (1, 1) oriented clockwise. (10 pts) Evaluate where C is the boundary of the square with vertices (0,0), (1,0),(0,1) and (1, 1) oriented clockwise.
(b) Evaluate the double integral e(y-2)/(y+2) dA where D is the triangle with vertices (0,0), (2,0) and (0,2). (Hint: Change variables, let u = y - x and v = y + x.)
14. (10 pts) Use Stokes' Theorem to compute F dr where F , y,) 32,5x, -2yand the curve C is given by the triangle with vertices (0,2,0), (3,0,0), and (0,0, 1) with positive orientation 14. (10 pts) Use Stokes' Theorem to compute F dr where F , y,) 32,5x, -2yand the curve C is given by the triangle with vertices (0,2,0), (3,0,0), and (0,0, 1) with positive orientation
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,...
2. (8 pts) Use Green's Theorem to evaluate fcln(1 + y) dx - triangle with vertices (0,0), (2,0) and (0,4). 17, dy, where C is the
3. Let S be the triangle with vertices at (0,0), (1,0) and (0,1). Let f (x, y) = e***. Use the change of variables u = x – y, v = x +y to find . f(a,y) dA.
with all steps shown? 5. Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. Prove dx dy. riangle A. [Hint: the lect when A is a rectangle. So, the idea is is to give a similar proof where we have this triangle A in place of a rectangle.] 3 marks 5. Let...