Integration Applications

This week we began Integral Applications, our fifth and final unit of AP Calculus. Integral Application is used to find the area bound by multiple functions, with respect to either X or Y.

When finding the area bound by two curves with respect to X, use this formula:

Example:

And when finding the area bound by two curves with respect to Y, use this one:

Example:

Tips:

• Always start by graphing the given functions if a graph isn't given.
• When the bounds are not explicitly stated, you can set the functions equal to each other and solve   for the values which will be your bounds.
• When there is no "bottom" function, you must integrate with respect to Y
• When the given functions switch positions, the integrals should be broken up so that the function that is on top acts as f(x).