Question
Asked Oct 17, 2019
101 views
Evaluate the triple integral.
 (x2 + y2) dx dy dz;
W is the pyramid with top vertex at
(0, 0, 2)
and base vertices at
(0, 0, 0),
(2, 0, 0),
(0, 2, 0),
and
(2, 2, 0)
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Expert Answer

Step 1

The given triple integral is,

S(y?)dchvdz
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S(y?)dchvdz

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Step 2

Here, the horizontal cross-section of the pyramid at height z is a square with one corner at (0, 0, z) and side length 2 – z.

So,...

22-2
L+)dxdyd=S S(+y)d«dydz
000
22-
dydz
+
3
(2
+(2-) dyd
3
0 0
-(2-2(2-2)
3
3
(2--)(2-)
(2
2-3(2-2
2(2-2)
3
j(2-ade
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22-2 L+)dxdyd=S S(+y)d«dydz 000 22- dydz + 3 (2 +(2-) dyd 3 0 0 -(2-2(2-2) 3 3 (2--)(2-) (2 2-3(2-2 2(2-2) 3 j(2-ade

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