1. Evaluate without integration: 1.2 2.12 3.6 4.21 5.Don’t know

2. Evaluate without integration: 1.4 2.7 3.14 4.22 5.Don’t know

3. Which of the following integrals does not make sense? 1. 2. 3. 4.

4. can be written as 1.True 2.False 3.Don’t know

5. What physical quantity does the surface integral represent if f(x, y)=1 ? 1.Integral represents the mass of a plane lamina of area A. 2.Integral represents the moment of inertia of the lamina A about the x - axis. 3.Integral represents the area of A.

6. What physical quantity does the surface integral represent if f(x, y)=y 2 ρ(x,y) ? 1.Integral represents the mass of a plane lamina of area A. 2.Integral represents the moment of inertia of the lamina A about the x - axis. 3.Integral represents the area of A.

7. What physical quantity does the surface integral represent if f(x, y)=ρ(x,y) ? 1.Integral represents the mass of a plane lamina of area A. 2.Integral represents the moment of inertia of the lamina A about the x - axis. 3.Integral represents the area of A.

8. If you change the order of integration, which will remain unchanged? 1.The integrand 2.The limits 3.Don’t know

9. Evaluate. 1.24 2.32 3.44 4.56 5.Don’t know

10. Evaluate. 1.3π-12 2.3π 3.5π 4.3π+12 5.Don’t know

11. Evaluate where V is the region enclosed by. 1.3 2.6 3.9 4.12 5.None of these.

12. Which diagram best represents the area of integration of. 1. 2. Don’t know 3.

13. Which diagram best represents the area of integration of. 1. 2. 3.4.

14. Which diagram best represents the region or integration of. 1.2. 3. 4.

15. Which diagram best represents the region or integration of. 1. 2. 3. 4.

16. Which diagram best represents the region or integration of. 1.2. 3. 4.

17. What double integral is obtained when the order of integration is reversed ? 1. 2. 3. 4.

18. What double integral is obtained when the order of integration is reversed ? 1. 2. 3. 4.

19. What double integral is obtained when the order of integration is reversed ? 1. 2. 3. 4.

20. Which of the following integrals are equal to ? 1. 2. 3. 4. 5.

21. Which of the following integrals is equal to ? 1. 2. 3. 4. 5.

22. Which dose not describes the graph of the equation r=cos θ ? 1.Line 2.Circle 3.Spiral 4.Rose

23. Convert the integral to polar coordinates : 1. 2. 3. 4.

24. Convert the integral to polar coordinates : 1. 2. 3. 4.

25. Integrate the function over the part of the quadrant in polar coordinates. 1. 2. 3. 4.

26. Which of the following integrals is equivalent to ? 1. 2. 3. 4.

27. Evaluate the integral. 1.0 2.17.63218 3.Cannot be done algebraically

28. Evaluate the volume under the surface given by z=f(x, y)=2xsin(y) over the region bounded above by the curve y=x 2 and below by the line y=0 for 0≤x≤1. 1.0.982 2.1.017 3.0.983 4.1.018

29. Evaluate f(x, y)=x 2 y over the quadrilateral with vertices at (0, 0), (3, 0), (2, 2) and (0,4) 1. 2. 3. 4.

30. Find the volume under the plane z=f(x, y)=3x+y above the rectangle 1.11/3 2.7 3.10 4.13 5.Don’t know

31. A tetrahedron is enclosed by the planes x=0, y=0, z=0 and x+y+z=6. Express this as a triple integral. 1. 2. 3. 4.

32. A tetrahedron is enclosed by the planes x=0, y=0, z=0 and x+y+z=6. Find the position of the centre of mass. 1. 2. 3. 4.

33. Which of the following represents the double integral after the inner integral has been evaluated? 1. 2. 3. 4.

34. Which of the following represents the double integral after the inner integral has been evaluated? 1. 2. 3. 4.

35. Find the moment of inertia about the y-axis of a cube of side 2, mass M and uniform density. 1. 2. 3. Don’t know 4.

36. Find the centre of pressure of a rectangle of sides 4 and 2, as shown, immersed vertically in a fluid with one of its edges in the surface. 1. 2. 3. Don’t know 4.

37. A rectangular thin plate has the dimensions shown and a variable density ρ, where ρ=xy. Find the centre of gravity of the lamina. 1. 2. 3. 4. Don’t know 5.