The mass of the rod is given by the linear density defined in kilograms as linear density*length.
The length of the rod is 4 m and the linear density is varying with `rho(x) = 5 + 2(x)^(1/2)`
The mass of the rod is the definite integral `int_(0)^4 rho(x) dx`
`int_(0)^45 + 2(x)^(1/2) dx`
=> `5x + 2*x^(3/2)/(3/2)` between 0 and 4
=> `5(4 - 0) + (4/3)(4^(3/2) - 0^(3/2))`
=> `20 + (4/3)*(8 - 0)`
=> `20 + 32/3`
=> `92/3`
The mass of the rod is `92/3` kg.
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now