__Monday April 24__

Solve,
write up and turn in:

Sec. 20.4: 39 a, g, 40

Calculate the
integral on the whole real line of the exponential of -x^2+2x

(Hint: complete the square.)

** Tuesday
April 25
Solve, write up and turn in:
Two
good practice problems. **You can check your answers using formulas
from geometry.

Calculate this integral in two ways:

Calculate this integral in two ways:

Sec. 20.5:

it may be helpful to sketch the region Ry separately, in an xz- plane.)

__Wednesday April 26__

Solve
the problems listed on yesterday's assignment.

** Thursday
April 27
Solve, write up and turn in:
Sec. 20.6: **1, 2, 11, 12, 15

__Friday
April 28__

Also, for an argument using algebra: the inequality containg theta is r^2<z<2r cos(theta) so cos(theta)>r/2>0 so cos(theta)>0.

to calculate the total volume removed from the sphere (rather than "of the cylindrical hole", which is too trivial).

Bonus problem (extra 6 points). Consider a domain D in the xy-plane, and a function f(x,y) defined on D.

Consider the region R bounded by the graph z=f(x,y) of f and the xy-plane. If f(x,y)>0 on D then we can calculate the volume of R in two ways:

as the double integral of f(x,y) dx dy on D, or as a triple integral of dx dy dz on V.

a) Show that the two numbers are equal.

b) What happens if f(x,y)<0 on D?

about center of mass, centroid (see formulas (7,8) in 20.3 for 2-d and p. 732 in 3-d).

Solve, write up and turn in:

Sec. 20

Sec. 20.6: 2a, 4, 6