Applications of the Fundamental Theorem

In This Chapter

  • Finding yet more curvy area
  • Integration’s Mean Value Theorem
  • Position equations and distance traveled
  • Functions defined by definite integrals
  • Pretending you’re Noah: finding arc length

Once you learned how to find the slope of a tangent line (a seemingly meaningless skill), it probably seemed as though the applications for the derivative would never stop. You were finding velocity and rates of change (both instantaneous and average), calculating related variable rates, optimizing functions, determining extrema, and, all in all, bringing peace and prosperity to the universe. ...

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