what is the answer to this? ### Problem StatementFind the mass (in kg) of the one-dimensional object.**Description:**A wire that is 5 meters long (starting at \( x = 0 \)) and has a density function given by:\[\rho(x) = x^2 + 5x \quad \text{kg/m}\]Calculate the total mass of the wire.### Solution ExplanationTo find the mass of the wire, we must integrate the density function over the length of the wire. The mass \( M \) is given by:\[M = \int_{0}^{5} \rho(x) \, dx\]Substituting \(\rho(x) = x^2 + 5x\), we have:\[M = \int_{0}^{5} (x^2 + 5x) \, dx\]Carrying out the integration:1. Integrate \( x^2 \) from 0 to 5:\[\int_{0}^{5} x^2 \, dx = \left[ \frac{x^3}{3} \right]_{0}^{5} = \frac{5^3}{3} - \frac{0^3}{3} = \frac{125}{3}\]2. Integrate \( 5x \) from 0 to 5:\[\int_{0}^{5} 5x \, dx = \left[ \frac{5x^2}{2} \right]_{0}^{5} = \frac{5 \times 25}{2} = \frac{125}{2}\]Adding both results:\[M = \frac{125}{3} + \frac{125}{2}\]Converting to a common denominator and adding:\[M = \frac{250}{6} + \frac{375}{6} = \frac{625}{6} \quad \text{kg}\]Therefore, the mass of the wire is approximately \( 104.17 \) kg.

Name: what is the answer to this? ### Problem StatementFind the mass (in kg)
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: what is the answer to this? ### Problem StatementFind the mass (in kg) of the one-dimensional object.**Description:**A wire that is 5 meters long (starting at \( x = 0 \)) and has a density function given by:\[\rho(x) = x^2 + 5x \quad \text{kg/m}\]Ca