1. INTEGRATION By: Sara Hershberger, Tony Tripp, & Brianna Booher

2. Basic Rules The whole goal is to find the exact area under a curve. Means the area between f(x) and the x-axis between x=a and x=b f(x) is called the integrand and a and b are called the limits of integration; a is the lower limit and b is the upper limit. The symbol dx has no official meaning by itself. The procedure of calculating an integral is called integration.

3. Properties 1. 2. 3. 4. 5. 6.

4. U-Substitution When a function is too complex, it needs to be rewritten to fit integration rules A “too complex” function is defined by a composition of functions Example:

5. U-Substitution If u = g(x) is a differentiable function whose range is an interval I and f is continuous on I then

6. Example 1

7. Example 2

8. Example 3

9. Example 4

10. Example 5

11. Area Under a Curve – The Definite Integral The integral sign represents integration.