Hint-if the integral of the absolute value is finite, then the order of integration does not matter; if we integrate first with respect to x and then with respect to y, we get the same result as if we integrate first with respect to y and then with respect to x.
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3...
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f : R3 +R be the function defined by f(x, y, z) = 1 - 2y + 3z. Using the change of variables theorem, rewrite Is f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
Don't give the same solution. Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3 +R be the function defined by f(x, y, z) = 2 - 2y + 3z. Using the change of variables theorem, rewrite Js f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1, 2, 3), and (-1,0,1). Let f: R3 R be the function defined by f(x,y, x) = x - 2y + 3z. Using the change of variables theorem, rewrite Ssf as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
6. Let S CR be the tetrahedron having vertices (0,0,0), (0, 1, 1), (1, 2, 3), and (-1,0,1). Let f:R3 → R be the function defined by f(x, y, x) = x – 2y + 3z. Using the change of variables theorem, rewrite Ss f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral (8 points).
Let S ⊆ be the tetrahedron having vertices (0, 0, 0), (0, 1, 1), (1, 2, 3), and (−1, 0, 1). Let f : → be the function defined by f(x, y, x) = x − 2y + 3z. Using the change of variables theorem, rewrite as an integral over a 3-rectangle, then use Fubini’s theorem to evaluate the integral. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image}
4. Let F(x, y, z)=(y,x,z2). Let S be the surface of the tetrahedron with the vertices (0,0,0), (2,0,0), (0,2,0), and (0,0,2). Use the divergence theorem to evaluate SS F.dS. (13 points)
2. Let S be the interior of the triangle with vertices (0,0,0), (1,0,0) and (0,1,0). a) Given F(x, y, z)=(x+1)i +(y+1)] +(2+1)k, calculate the flux of through S without using an integral b) F(x, y, z) = (z+1)7 +(y+1) 7+(x+1)k , set up an iterated integral in dx dy or dy dx to calculate the flux of F through S. You do not need to evaluate your integral
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices (1,1,1), (2,1,1) and (3,2,2), traversed from ,1) to (2,1,1) to (3,2,2) to (1,1,1). Evaluate F.dr Justify your answer (c) Find a function p: R3R such that F Vp. (d) Evaluate dr, where Г is the path y-12, z-0, from (0,0,0) to (2,4,0) followed by the line seqment from (2, 4,0 to 1, 1,2) 3. Let (a) Show that F is conservative...
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
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...