NAME I.D.: 8. Evaluate the double integral where D is the square with vertices (0.2), (1.1),...
(1 point) Evaluate the double integral || 6xydA, where D is the triangular region with vertices (0,0), (1, 2), and (0,3). Answer:
(1 point) Evaluate the double integral / = - SD xy A where D is the triangular region with vertices (0,0), (4,0), (0,5).
Evaluate the integral 5. Ten dz, where C is the boundary of the square with vertices at the points 0, 1, 1+i and i, with a counter clockwise orientation. What is the integral over the reverse contour?
Evaluate the double integral I = Slo xy dA where D is the triangular region with vertices (0,0), (1,0), (0,6).
(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.)
1. (4 points) Evaluate the double integral on the given domain D xy where D={(x,y):25x54,15ys3} 2. (4 points) Evaluate the double integral on the given domain S dxdy © 1(x2 + y2)3 where D=(x,y):15x2 + y2 <4, yzo}
6. Use the additivity of the double integral to evaluate the double integral of f(x,y) = x2-y2 over the region that is a disk x2 + y2 < 4 with a triangular hole with vertices (0,0), (0,1), and (1,1).
Use a change of variables to evaluate the double integral below,
where D is the region bounded by the four lines
y − x=0
y − x = 5
y + x = 2, and
y + x = 4:
(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.
Evaluate the triple integral. JJJr Oya, where is the solid tetrahedron with vertices (0,0,0), (1,0,0), (1,1,0), and (1,0,4).