Evaluate ZC x2y2dx + 4xy3dy where C is the triangle with vertices (0,0), (1,3), and (0,3). (b) Do not use the Green’s Theorem.
Evaluate ZC x2y2dx + 4xy3dy where C is the triangle with vertices (0,0), (1,3), and (0,3)....
the base of a solid is the triangle in the xy-plane
with vertices (0,0), (2,0), (0,3). The cross-sections of the solid
perpendicular to the x-axis are squares with sides in the xy-plane.
Find the volume of this solid.
The base of a sold is the triangle in the type with rices (0,01.(2.0),(0,3) The cross sections of the son parastareas are roures with sides in the xy-plane Find the volume of this solid (HINT: Do not include unnecessary spaces or decimal...
5. Evaluate SS x+2y da where R is the triangle with vertices (0,3), (4,1), and (2,6). Use the transformation x=-(u- *=£cu-v),= (3u+v+12). 6. Evaluate S 2 ydx+(1 – x)dy along the curve C given by y=1 –x" from x = -1 to x = 2.
4. Evaluate (2 + y)dA, where D is the triangle with vertices (0,0), (0,1),(1,0).
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
(10 pt) Evaluate rydx + x?y dy where is the triangle with vertices (0,0), (1,0),(1, 2) with positive orientation. fo
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
(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.)
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the point (1, 0, 0)
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the...
9.) (12 pts.) Let loop C be the triangle with vertices (0,0), (2,0), and (2,6). Evaluate the line integral $ ay dx + (x - y) dy using one of Green's Theorems.
2. Evaluate the line integral fxydx + xºy’dy where C is the triangle with vertices с (0, 0), (1, 0), (1, 2) by: (1) Direct integration (ii) Green's theorem [2/3]