Question

Find the mass of the thin bar with the given density function.
P(x) = 4 if 0 4+x if 3

Answer 1

The mass of the thin bar is 21 units.

Step-by-step explanation:

To find the mass of the thin bar, we need to integrate the density function over the length of the bar. Since the density function is different for different intervals of x, we need to split the integral into two parts.

For 0 < x < 3, the density is constant at 4. So the mass of this interval is given by:

m1 = density * length = 4 * (3 - 0) = 12.

For 3 < x < 4, the density is given by 4+x. So the mass of this interval is:

m2 = ∫ density * length = ∫ (4+x) * dx = ∫ (4+x) * dx = |2x+x^2| from 3 to 4 = |2(4)+4^2| - |2(3)+3^2| = 24 - 15 = 9.

Therefore, the total mass of the thin bar is m1 + m2 = 12 + 9 = 21.