Indefinite Integrals

Find The Antiderivatives o Antiderivatives- The inverse of the derivative o Denoted as F(x) o Leibniz Notation: (indefinite integral)

Finding Antiderivative (Power/Polynomial Rule) 1)Add one to the exponent ***If you have just a constant, add an X 2)Divide coefficient by new exponent 3)Add a C (constant term) 4)Simplify (if needed)

Examples 1) 2)

Substitution To Find Antiderivatives You can use substitution when the following scenarios exist: 1)Quantity raised to a power 2)Trigonometric ration of an unusual angle 3)Trigonometric ratio raised to a power Steps: 1)Let “u” equal the quantity 2)Find du/dx 3)Match/manipulate du/dx to the original function 4)Substitute 5)Find the Antiderivative in terms of “u” 6)Re-substitute for “x”

Examples

Using Substitution to Find Antiderivatives of Trigonometric Ratios Raised to a Power Steps: 1)Let “u” equal the trigonometric ratio raised to the power 2)Complete the substitution procedure EXAMPLE :

Using Substitution to Find Antiderivatives with Trigonometric Ratios with Unusual Angles Steps: 1)Let “u” equal the angle 2)Complete the substitution procedure EXAMPLE :

Solving for C (constant term) o After finding the Indefinite Integral, if given an interval such as (3,4), you can plug those values into the equation o Solve for C o Re-write the new equation with the C value o EXAMPLE: