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Integral Rules

For the following, a, b, c, and C are constants; for definite integrals, these represent real number constants. The rules only apply when the integrals exist.

 

Indefinite integrals (These rules all apply to definite integrals as well)

1.

2.

3.

4.

5. Integration by parts:

 

Definite integrals

1.

2.

3. If f(u) g(u) for all a u b, then

4. If f(u) M for all a u b, then

5. If m f(u) for all a u b, then

6. If a b, then

 

See also

Integral table, integration methods , derivative rules

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes