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Modeling with Integral Applications
Worksheet
Grade Level
Calculus II
CAL2.76 Modeling with Integral Applications
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A vertical semicircular plate of radius 4 meters has its diameter along the water surface and extends downward. At depth y, 0 <= y <= 4, its width is 2sqrt(16-y
2
). Which integral gives the hydrostatic force? Use gamma for water weight density.
A
gamma∫_0
4
2sqrt(16-y
2
) dy
B
gamma∫_0
4
y·2sqrt(16-y
2
) dy
C
gamma∫_0
4
y
2
·2sqrt(16-y
2
) dy
D
gamma∫_-4
4
(4-y)2sqrt(16-y
2
) dy
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