The Fundamental Theorem of Calculus explanations, examples, practice problems. Ready? Let's do this.
Integrating the Velocity Function
When Velocity is Non-NegativeAgain, let's assume we're cruising on the highway looking for some gas station nourishment. We could actually figure out the distance we've travelled by knowing our vel...
About the Fundamental Theorem of Calculus (FTC)
If s(t) is a position function with rate of change v(t) = s'(t), thenbecause both of these quantities describe the same thing: s(b) – s(a)is the difference between the starting position at t = a...
Using the FTC to Evaluate Integrals
If f is the derivative of F, then we call F an antiderivative of f. We already know how to find antiderivatives–we just didn't tell you that's what they're called. It's like when you realize what...
Units
Velocity is the rate of change of distance, and is measured inWhen we integrate velocity over a specific time interval, we get the distance traveled over that interval.The definite integral c...
Word Problems
Word problems involving integrals usually fall into one of two general categories: alien related and non-alien related. The non-alien related ones are totally the worst. Here's how to figure them...
The Second Fundamental Theorem of Calculus
As if one Fundamental Theorem of Calculus wasn't enough, there's a second one. The first FTC says how to evaluate the definite integralif you know an antiderivative of f. The second FTC says how to...
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 un...