Ch 6. Integrals Multimedia Engineering Math IndefiniteIntegral Area DefiniteIntegral FundamentalTheorem SubstitutionRule
 Chapter 1. Limits 2. Derivatives I 3. Derivatives II 4. Mean Value 5. Curve Sketching 6. Integrals 7. Inverse Functions 8. Integration Tech. 9. Integrate App. 10. Parametric Eqs. 11. Polar Coord. 12. Series Appendix Basic Math Units Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Hengzhong Wen Chean Chin Ngo Meirong Huang Kurt Gramoll ©Kurt Gramoll

 MATHEMATICS - CASE STUDY SOLUTION The Linear Density Function of the rod The linear density of a non-homogeneous rod is expressed as ρ(x) = x2 - x + 3 with unit of g/m. If the rod length is 4 m, what is the mass of the rod? If the rod is divided into many small pieces, the total mass of the rod is the sum of the mass in each piece, which can be expressed as       When the rod is divided into infinite small pieces, the result is the exact mass value. The Low and Upper Limit of rod The definite integral definition gives       Therefore,       in which x1 and x2 are the start and the end of the rod. Substituting x1 = 0, x2 = 4, and ρ(x) = x2 - x + 3 into the above formula gives