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."
Images of prominent female athletes

 

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.