The mass of a rod varies in such a way that the mass of a piece x meters long, measured from the left end, is $x ^ { 2 }$ kilograms. Find the density in kg/m at the point 2 meters from the left end.
A)1
B)5
C)3
D)4
E)7
F)6
G)2
H)8

Question

Quizplus · Accepted Answer

The density at a point is given by the derivative of the mass with respect to length, which is $ \frac{d}{dx}(x^2) = 2x $. At $ x = 2 $ meters, the density is $ 2 \times 2 = 4 $ kg/m.

The Mass of a Rod Varies in Such a Way x2x ^ { 2 }x2

The Mass of a Rod Varies in Such a Way $x ^ { 2 }$