Sin()ddy, where the boundary of R is the trapezoid 2. Evaluate with vertices (1,1), (2,2), (4,0),...
(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.)
Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1, y-x +4 y#2x+2y»2x + 5 A) -5 B) 10 C)5 D)-10 32) y+ x where R is the trapezoid with vertices at (6,0), ,0).。. 6), (0.9) 45 45 B) ÷ sin l 45 C) sin 2 45 A) sin 2 Use the given transformation to evaluate the integral. -5x dx dy where R is the parallelogram bounded by the linesy-x+1,...
CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1), and (1,1). Consider the following integral: 4(x y)e- dA. R Choose a substitution to new coordinates u and v that will simplify this integrand. Draw a sketch of both the region R and the image of the region in the u,v-plane. Evaluate the integral in the new coordinate system. Warning: No matter what strategy you use for this integral, it will require at least...
id with vertices (0,0,0), (0,1,0), (11,0), Evaluate /sin(y3) dV where S is the pyram (1,1, 1) and (0,1,1).
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
(15 pts) Find (2x - y) dA, where R is the triangular region with vertices (0,0), (1, 1), and (2, -1). Use the change of variables u = x - y and v = x + 2y.
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
Use the given transformation to evaluate the given integral, where R is the parallelogram with vertices (-2, 6), (2, -6), (5,-3), and (1,9). L = SUR(16.+12y) dA; r = {(u +v), y=(v – 3u) L =
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.