Properties of Integrals

Here is a list of properties that can be applied when finding the integral of a function. These properties are mostly derived from the Riemann Sum approach to integration.

Additive Properties

When integrating a function over two intervals where the upper bound of the first is the same as the first, the integrands can be combined. Integrands can also be split into two intervals that hold the same conditions.

If the upper and lower bound are the same, the area is 0.

If an interval is backwards, the area is the opposite sign.

Multiplying by a Constant "c"

Constants, such as coefficients, can be distributed out of the integrand and multiplied afterwards.

Integrating a Sum

The integral of a sum can be split up into two integrands and added together

Finding Total Area Within an Interval

To find the total area, use the absolute value of the integrand.

Inequalities