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Mass from Density in One Dimension
Worksheet
Grade Level
Calculus II
CAL2.75 Mass from Density in One Dimension
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A chain occupies 0 ≤ x ≤ 9 meters, with x measured from the left end. Its density is 6 - (1/3)r kg/m, where r is the distance from the right end. Using x as the variable, which integral gives the mass of 1 ≤ x ≤ 6 in kilograms?
A
∫_{1}
6
(6 - (1/3)x) dx
B
∫_{1}
6
(6 - (1/3)(9 - x)) dx
C
∫_{0}
9
(6 - (1/3)(9 - x)) dx
D
∫_{1}
6
(x(6 - (1/3)(9 - x))) dx
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