Antiderivatives.
Antiderivatives do the opposite of what a derivative does. When solving integrals we are trying to undo the derivative. There are two types of integrals. Definite and indefinite integrals. Integrals can be used to find the area under a curve.
Definite integrals:
For definite integrals, you take the antiderivative of a derivative on a given interval. We can solve for the exact integral by using the fundamental theorem of calculus. Definite integrals will give us the exact area of a curve when we solve on a restricted domain. The following is what a indefinite integral looks like from a to b.
Definite integrals:
For definite integrals, you take the antiderivative of a derivative on a given interval. We can solve for the exact integral by using the fundamental theorem of calculus. Definite integrals will give us the exact area of a curve when we solve on a restricted domain. The following is what a indefinite integral looks like from a to b.
Indefinite integrals:
Similar to definite integrals, the goal of indefinite integrals is to also find the antiderivative, but not specific to an interval. The antiderivative of indefinite integrals are always followed by a +c since the constant is always unknown.
Similar to definite integrals, the goal of indefinite integrals is to also find the antiderivative, but not specific to an interval. The antiderivative of indefinite integrals are always followed by a +c since the constant is always unknown.
The following are a list of integrals that can be used to find antiderivatives. (List from Math UCLA).
List of antiderivative properties. (From Paul's Online Math Notes)