6.1 Antiderivatives

Antiderivatives!!
If we are given a derivative, how do we find the original function

A function F is an antiderivative of f if F'(x) = f(x)
...in other words the derivative of your integral equals the original function

Basic Rules

1. The Antiderivative of a Constant k

2. The Power Rule


3. The Antiderivative of a Multiple of a Function

4. The Sum Rule


5. The Antiderivatice of the Exponential Function

6. The Antiderivative of f(x)= 1/x

You can also find the value of C when given an integral and a point.

Initial Value Problem

Example:

plug in your point


therefore...

Helpful websites:

• http://www.calc101.com/webMathematica/integrals.jsp
• this one actually can help you check your homework answers

• http://archives.math.utk.edu/visual.calculus/4/antider.1/
• http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorials4/frames6_1.html
  

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