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Unformatted text preview: is a box with
base A and height 3. Its volume, therefore, is
given by
length × width × height
= (7 − 2) × (4 − 2) × 3 .
Consequently, 2. I = 72 cu. units correct
3. I = 70 cu. units
4. I = 68 cu. units
5. I = 69 cu. units
Explanation:
The double integral I = 30 . I= f (x, y ) dxdy
A keywords: volume, double integral, rectangular region, rectangular solid
002 10.0 points is the volume of the solid below the graph of
f having the rectangle
A= (x, y ) : 0 ≤ x ≤ 6, 0 ≤ y ≤ 4 chester (crc2876) – HW13 – meth – (91845)
for its base. Thus the solid is the wedge Explanation:
Since x varies but y does not,
2 z 2 x − 4 x2 y d x = I=
0 6 2 12 43
x − xy
2
3 0 . Consequently,
y
I = 2− 32
y.
3 (6, 4)
6 x and so its volume is the area of triangular
face multiplied by the thickness of the wedge.
Consequently, keywords:
004 10.0 points Determine the...
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This note was uploaded on 08/25/2013 for the course MATH 408M taught by Professor Kushner during the Summer '10 term at University of Texas at Austin.
 Summer '10
 KUSHNER
 Multivariable Calculus

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