Miscellaneous (not Math)
The day and time of your final for this class?
What is Wednesday of finals week (December 11) at either 7 am or 10 am?
The double integral over the region enclosed by the curves y = x^2 and y = 3x for the function f(x,y) = xy
What is 243/8 ?
The point that is the center of mass of a sphere of radius 6 with the density function f(x,y,z) = 1
What is the point (0,0,0) ?
The integrating factor that must be added to dr d(theta) when integrating in polar coordinates
What is 'r' ?
The bounds in spherical coordinates for a quarter sphere of radius 6
What is 0<p<6, 0<phi<pi/4 , 0<theta < pi/2 ?
The amount of protein in a single slice of Costco cheese pizza?
What is 40 grams?
The interpretation of a double integral over a region D with a function = 1
What is the area?
The volume of a 3D shape D (using triple integrals)
What is the triple integral over a region D with the function f(x,y,z) = 1?
The double integral of x^2 + y^2 over the quarter circle (in the first quadrant) of radius 3
What is 81*pi / 8
The equation for the cone z = sqrt(x^2 + y^2) is spherical coordinates
What is phi = pi/4?
The writer of 1984
Who is George Orwell?
Switch the order of integral for the integral -2 < y < 2 0 < x< sqrt(4-y^2) to an integral with order dy dx
*Use arbitrary fxn f(x,y)
What is the integral with 0 < x < 2 and - sqrt (4 - x^2) < y < sqrt(4 - x^2) ?
The interpretation of a density function f(x,y,z), triple integrated over a region E
What is the weight of the shape E?
The volume of the solid bounded by the paraboloid z = 1 + 2x^2 + 2y^2 and the plane z = 7 in the first octant
*Hint: where do they intersect
What is 9/4 * pi ?
The description of the solid (or sketch) described by the inequalities
1 < p < 2 and pi/2 < phi < pi
What is a solid region between the spheres of radius 1 and 2 below the z axis ?
The World Series winner in 2016
Who are the Chicago Cubs?
The volume of the solid bounded by the cylinder y^2 + z^2 = 4, and the planes x = 2y, x=0, z= 0 in the first octant
What is 16/3 ?
Evaluate the integral
int (0 to 1) int (0 to 1) int (0 to sqrt(1-z^2))
function = z / (y + 1)
dx dz dy
What is 1/3 * ln(2) ?
The bounds in cylindrical coordinates (use a triple integral) for the volume that lies between the cylinders x^2 + y^2 = 1 and x^2 + y^2 = 16
above the xy plane and below the plane z = y + 4
What is
0<z< rsin(theta) + 4
1 < r < 4
0 < theta < 2*pi (for r * dz dr d(theta)) ?
Evaluate the triple integral to find the volume between the between the two spheres x^2 + y^2 + z^2 = 4 and x^2 + y^2 + z^2 = 9
What is 24*pi?
The actor who plays Colonel Kurtz in the 1979 movie Apocalypse Now as well as Vito Corleone in the 1972 movie The Godfather
Who is Marlon Brando?
Reverse the order of integration of the double integral and compute
Region: 3y < y < 3 and 0 < x < 1 (dx dy)
Function: f(x,y) = e ^ (x^2)
What is (e^9 - 1) / 6 ?
The volume of the solid enclosed by the cylinder y = x^2 and the planes z = 0 and y + z = 1
*Hint: what does the xy plane look like
What is 8/15 ?
Set up the iterated integral to find the volume of the solid enclosed by the paraboloids y = x^2 + z^2 and y = 8 - x^2 - z^2
Hint* Use cylindrical but with y instead of z
What is dy dr dtheta
x^2 + z^2 < y < 8 - x^2 - z^2
0 < r < 2
0 < theta < 2pi
The volume enclosed by p = csc(phi) and the planes z = 1 and z = -1
Hint* x^2 + y^2 = (psin(phi)) ^ 2
What is 2pi ?