The region R = {(x, y) E R2Iy > 0, x2 + y < 2} can be described in polar coordinates by : %3D {(r, 0)|0
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- Use Green's Theorem to evaluate∮tan^-1(y)dx-(xy^)/(1+y^2) dy where C is the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1) and oriented counterclockwise. A. -1 B. 2 C. 1 D. -2Evaluate the triple integral. 3xyz dV, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0, 1)Determine a region of the xy-plane for which the given differentail equation would have a unique solution whos graph passes through point (x,y) in the region. (y-x)y' = y +x
- Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices (0,0,0),(7,0,0),(0,7,0),(0,0,7).Let u(x,y) satisfy the following equationuxx+(x2+y2-1)uyy=0Find the region in which the equation is elliptic and the region in which the equation is hyperbolic.Use Green’s theorem to evaluate ∮C(ye2xy−5y)dx+ (xe2xy−2x)dy, where Cis the counterclockwise oriented boundary curve of the square with vertices at(0,0), (0,1), (1,0), and (1.1).
- The solid generated by revolving the regionbounded by the graphs of x = , y = 0, andx = 2 about the y-axis isIn isosceles triangle XYZ, XY = YZ = 10, and XZ = 16. Where C is the centroid of triangle XYZ, find the distance from C to side XZ of the triangle.Find the region generated by rotating the region bounded by xy=1, x=1, x=2 and y=0 around the y-axis