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- 5. Find the centroid of the region bounded by the curves y = x6 and x = y6.Let D be the triangular region in the xy-plane with vertices (1,0), (0.1) and (3/2, 1/2) Use a suitable change of variables to calculate the integral (image)What is the absolute extrema of Q(y,z) = y2z2 on a region with vertices at the points (0,0), (0,4) and (4,0)?
- If the components of have continuous second partialderivatives and is the boundary surface of a simple solidregion, show that xxS curl F dS 0Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(2,0,0),(0,6,0),(0,0,4)A solid is obtained by rotating the shaded region about the specified line Line x = -2
- Show that the image of the annulus {1<|z|<2} under w=2/(z-1) is the domain {W: Re(W)>-1, |W=2/3|>4/3} using Möbius transformation.Find the centroid of the region bounded by the given curve. x = 5-y2 ; x = 0Find exact coordinates of the centroid of the region bounded by the given curves. y = x + 20, y = x2
- 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 +xS is the region bounded by paraboloid z=9-x^2-y^2 and the xy planeFind the image of the rectangular region in the z − plane formed by joining the points0, 0 , 2, 0 , 2, 1 , (0, 1) in the w − plane under the transformation,w = (1 +i )z − 2iInterpret both the regions graphically.