Section 12-3

Multiple Integration

I. Double Integration

f (x,y)dxdy a

b

c

d

Evaluate the inside with respect to dx treating y as constant then evaluate the outside with respect to dy treating x as constant.

Double integration yields _________________

1.

9x 2ydxdy 2

3

1

2

2.

8x 2ydydx 1

2

2

3

II. Triple Integration

f (x,y,z) dxdydza

b

c

d

r

s

Work from the inside out

Triple integration yields ______________

3.

0

3x

4dzdydxy

x2

2

5

4.

V dldwdh0

3

0

2

0

1

Assignment:

Practice 12-3