CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1),...
5 ve 6. Soru Dry - xdA over the triangle with vertices ( -1,0), (0,0) and (0,1) changing the variables by u = y - x and v = y + x. (DONOTEVALUATE INTEGRAL) 1 w 5. (15 points) Write the integral representing the area of the region al < x2 + y2 < band below the line y = x in polar coordinates.(DONOT EVALUATE INTEGRAL) ,y,z) as an iterated integral in cartesian coor- dinates. E is the region inside...
Q3. If R is the triangle with vertices (2,0), (6,4) and (1,4), then draw the region R' after applying the transformation x = (u – v), y =(u + 40). Also, write the limit for integration in both region, i.e. Ne f(x,y) dA = write the limit for x,y and then covert the integration with limit in R' ?
(1 point) Set up a double integral for calculating the flux of F -4xi + yj + zk through the part of the surface z =-2x-4y + 4 above the triangle in the xy-plane with vertices (0,0), (0,4), and (2,0), oriented upward. Instructions: Please enter the integrand in the first answer box. Depending on the order of integration you choose, enter dx and dy in either order into the second and third answer boxes with only one dx or dy...
Let the region R be the triangle with vertices (1, 1), (1,3), (2, 2). Write the iterated integrals for SSR f(x, y)dA 1. in the “dydx” order of integration 2. in the “dxdy” order of integration
3. (2 Points) Let Q be the quadrilateral in the ry-plane with vertices (1, 0), (4,0), (0, 1), (0,4). Consider 1 dA I+y Deda (a) Evaluate the integral using the normal ry-coordinates. (b) Consider the change of coordinates r = u-uv and y= uv. What is the image of Q under this change of coordinates?bi (c) Calculate the integral using the change of coordinates from the previous part. Change of Variables When working integrals, it is wise to choose a...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
20. Show that the second derivative test is inconclusive when applied to f(r, y) 2 at (0,0). Describe the behavior of the function at the critical point For the next few exercises things to know are: 1. In a closed and bounded region, a continuous function will assume a maximum value and it will assume ImIIm valuic. 2. These values have to be assumed either at a critical interior point or on the boundary. They canot be assumed anywhere else....
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)...
Can you do 3 and 6 Determine whether the following assertions are true or false 1. The double integral JJDy2dA, where D is the disk x2 +y2く1, is equal to π/3 2. The iterated integral J^S 4drdy is equal to 3. The center of mass of the triangular lamina that occupies the region D- 10 4. The triple integral of a function f over the solid tetrahedron with vertices (0,0,0), x < 3,0 < y < 3-2) and has a...
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...