ASSIGNMENT

ASSIGNMENT QUESTIONS 1. Find the area of the region bounded by the parabola y2=4ax and the line x+y=3a in the positive quadrant 2. Change the order of Integration in   a ax a x dx dy xy 2 0 3 4 2 and then Evaluate it 3. By changing the order of integration evaluate   a ax dx dy x 0 2 0 2 4. Evaluate      0 x y dx dy y e by changing the order of integration 5. Evaluate    1  0 0 0 x x y zdzdydx 6. Evaluate  V dxdydz , where V is the finite region of the space (tetrahedron) Formed by the planes x=0, y=0, z=0 and 2x+3y+4z=12 7. Find the volume of the ellipsoid 1 2 2 2 2 2 2    c z b y a x 8. The temperature of points in space is given by T x y z  x  y  z 2 2 ( , , ) . A mosquito located (1 ,1, 2)desires to fly in such a direction that it will get warm as soon as possible. In what direction should it move? 9. Prove that =(x2-y2+x) -(2xy+y) is a conservative field and find the scalar potential of . 10. Using Greens theorem, evaluate          C 3x 8y dx 4y 6xy dy 2 2 where C is the boundary of the triangle formed by the lines x=0,y=0, x+y=1 in the xy plane. 11. Verify Gauss divergence Theorem for = taken over the cube bounded by the planes x= 0, x = 1, y = 0, y = 1, z = 0, z = 1 12. Verify Gauss divergence theorem for ( ) ( ) ( ) . 2 2 2 F  x  yz i  y  xz j  z  xy k and S is the surface of the rectangular parallelepiped bounded by x  0, x  a, y  0, y  b, z  0and z  c . 13. Under the transformation z w 1  ,find the image of 22i z 14. Find the bilinear transformation which maps  ,i,0 onto 0,i,  15. Find the bilinear transformation which maps the points z=-1,0,1 into the points w=0,i,3i.