# The Fundamental Theorem of Calculus

# The Fundamental Theorem of Calculus Exercises

#### 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 travelled over that interval.The definite integral ...

#### 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 o...

#### 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...