Integration

What does integration mean? Antiderivatives of a function are called indefinite integrals. When we find these indefinite integrals we are integrating. That is, if we have information about a first derivative we can recover the original function. Essentially we are trying to find where these expressions came from. If the information is velocity, what will integration allow you to find?

What does integration look like? To start with, just ask yourself “where did this derivative come from?”

Basic problems

The reverse of the power rule Since , then the integration will go up by 1. That is,

Things to remember Always tack on “+ c” at the end. Since the derivative of a constant = 0, the “+ c” takes care of that. Constants can be brought out in front of an integration. They don’t impact anything so they just go along for the ride. If the function u is “elaborate” look for “du” to be tacked on at the end.

What did that last one say? If the function u is “elaborate” look for “du” to be tacked on at the end. The easiest way to do a problem like this is called u substitution.

The Rule Where f and g’ are continuous functions. Sub u=g(x) and du=g’(x)dx to get Integrate with respect to u Replace u with g(x)

So lets look at this again Remember: if there is an elaborate function, let it equal u and then find du

More Sample Problems

More Sample Problems