if you wish you can also turn in a (better) solution on Apr.24)

Wednesday
April 19

Solve Examples 1,2, 3 page 721.

Solve:

Sec. 20.2: 1, 3

Sec. 20.1: 1, 3,15

Sec. 20.3: Find the
mass only: 1

Solve,
write up and turn in:

Sec. 20.2: 2 ,5, 17

Sec. 20.1: 2, 8, 16, 18, 22

Sec. 20.3: Find the mass only: 3, 7

Thursday
April 20

Sec. 20.1: 25, 27

Sec. 20.2: 7, 8, 10

Friday
April 21

a) A.20 formulas (5),(6).; in formula (7) we wrote the absolute value of the Jacobian rather than the Jacobian itself.

We also saw the argument on page 844.

b) Sec. 20.4 (Example 3 will be discussed on Monday.)

Solve, write up and turn in:

Sec. 20.4: 3, 12, 15, 23, 28, 31 a

Bonus problem (extra 5 points)

Explain why we do not need to use absolute value of dx/du in substitutions

in one-dimensional integrals: dx = (dx/du) du.

Hint: use as an example, the integral between 0 and 1 of dx;

then substitute x=-2u. To make the substitution similar to the two-dimensional case,

think of your integral as an integral on the segment [0,1] (which is a region R). What is D in this example?