The Fundamental Theorem of Calculus
In the Real World
We could try to point out different careers in which you need to use what we've just been doing, but we're not going to bother. Let the textbooks do that.
A large part of the practicality of this unit lies in the way it stretches your brain. Thinking backwards to find antiderivatives and understanding the FTC are exercises that will help your general thinking and problem-solving skills. Also, if you understand this stuff first then you can help that cute boy/girl in your class who's having trouble. What could be more practical than that?
On a more immediate note, you're going to need these tools for the rest of calculus. When we get to density and probability, for example, a lot of questions will ask things like
"For what value of M is
Practice now, save yourself headaches later!