Evaluate without integration: 2 12 6 21 Don’t know

Evaluate without integration: 4 7 14 22 Don’t know

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

can be written as True False Don’t know

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

What physical quantity does the surface integral represent if f(x, y)=y2ρ(x,y)? Integral represents the mass of a plane lamina of area A. Integral represents the moment of inertia of the lamina A about the x-axis. Integral represents the area of A.

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

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

Evaluate . 24 32 44 56 Don’t know

Evaluate . 3π-12 3π 5π 3π+12 Don’t know

Evaluate where V is the region enclosed by . 3 6 9 12 None of these.

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

Which diagram best represents the area of integration of . Enter answer text... Picture Choice 2 Picture Choice 3 Picture Choice 4 1. 2. 4. 3.

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

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

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

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

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

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

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

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

Which dose not describes the graph of the equation r=cos θ? Line Circle Spiral Rose

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

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

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

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

Evaluate the integral . 17.63218 Cannot be done algebraically

Evaluate the volume under the surface given by z=f(x, y)=2xsin(y) over the region bounded above by the curve y=x2 and below by the line y=0 for 0≤x≤1. 0.982 1.017 0.983 1.018

Evaluate f(x, y)=x2y over the quadrilateral with vertices at (0, 0), (3, 0), (2, 2) and (0,4) 1. 1 2 3 4 2. 3. 4.

Find the volume under the plane z=f(x, y)=3x+y above the rectangle 11/3 7 10 13 Don’t know

A tetrahedron is enclosed by the planes x=0, y=0, z=0 and x+y+z=6 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. 1 2 3 4 2. 3. 4.

A tetrahedron is enclosed by the planes x=0, y=0, z=0 and x+y+z=6 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. 1 2 3 4 2. 3. 4.

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

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

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

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. 1 2 3 4 3. 2. Don’t know 4.

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 5 1. 2. 3. 4. Don’t know 5.