1-D Integration and Centroids
Integral of a function:The integral of a function f(x) over an interval from x1 to x2 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: