 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 Original Produce Rate Substitution Function for theProduce Rate Function Lansing automobile company is manufacturing a new model of car with a produce rate of How many cars can be produced in the first season? The output of the car is the integral of the production rate with respect to time in the range between 0 and 3 months. Let u = t + 20. The derivative of u with respect to time t is      du/dt = 1 Rearrange the above equation gives      du = dt The new limits of integration can be calculated. When t = 0, u = 20 and when t = 3, u = 23. The substitution rule gives that Thererfore, 