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=<br />
2<br />
∫∫<br />
D zx<br />
8<br />
−<br />
x<br />
2<br />
−<br />
zdzdx<br />
=<br />
2<br />
∫<br />
2<br />
−2<br />
2<br />
2<br />
d<br />
x<br />
∫<br />
8−<br />
x2<br />
0<br />
8<br />
−<br />
x<br />
2<br />
−<br />
z d z<br />
=<br />
4<br />
3<br />
2<br />
∫ − 2<br />
令 x<br />
2<br />
2<br />
( 8 − )<br />
3<br />
2<br />
d<br />
= 2 2sint,dx<br />
=<br />
8<br />
3<br />
x x = ∫ ( 8 − x )<br />
2<br />
0<br />
2<br />
2<br />
2costdt<br />
2 3<br />
d<br />
x<br />
π<br />
8<br />
=<br />
2<br />
0<br />
3<br />
( 2 2 )<br />
∫ cos t ×<br />
3<br />
3<br />
2<br />
2 cos<br />
tdt<br />
π<br />
8<br />
= × 64 ∫<br />
2<br />
3 0<br />
cos<br />
4<br />
tdt<br />
=<br />
8 3 1<br />
× 64 × × ×<br />
π<br />
3 4 2 2<br />
=<br />
32 π
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