1-D Integration and Centroids

**Integral of a function:** The integral of a function *f(x)* over an interval from *x*_{1 }to *x*_{2} yield the area under the curve in this interval

Note: The integral represents the as .

**Indefinite Integrals to know []:**

**Note: **Remember to add a constant of integration if you are not specifying limits. You evaluate the constant of integration by forcing the integral to pass through a known point.

**Note: **For definite integrals subtract the value of the integral at the lower limit from its value at the upper limit. For example, if you have the indefinite integral

where *C* is the constant of integration which drops out of the final expression.

**Note:** The following notation is common

Integration by parts:

**Centroid of an area: The centroid of an area is the area weighted average location of the given area.**

Centroids of common shapes: