Areas Between Curves: Apply It

  • Calculate the area between two curves by integrating with respect to [latex]x[/latex]
  • Calculate the area of a compound region
  • Calculate the area between two curves by integrating with respect to [latex]y[/latex]
  • Determine the most effective variable, [latex]x[/latex] or [latex]y[/latex], for integration based on the curves’ orientation

Sydney Michelle McLaughlin-Levrone and Femke Bol are track and field athletes who both hold world records and compete in sprint events.

On the left, McLaughlin-Levrone competing at the 2022 World Athletics Championships, running on a track with a focused expression. On the right, Bol smiling and holding her gold medal for the 400m hurdles at the 2023 World Championships in Budapest."

 

Suppose they were to run a long distance race rather than a sprint. In a sprint, runners accelerate quickly and maintain a very high velocity for a relatively short distance, whereas in a long distance race, endurance is key, and so runners must take a different approach to velocity and acceleration.