AP Calculus BC glossary
Integral test
The integral test says that for a positive, decreasing, continuous function, the series of its values and the improper integral of the function either both converge or both diverge. It is what proves the p-series rule.
All three conditions must be checked and stated: the function must be positive, decreasing, and continuous on the interval of interest. Skipping the verification is a common way to lose credit even with a correct conclusion.
The integral is not the sum
The test tells you whether the series converges, not what it converges to. The value of the integral is generally not the sum of the series.
Appears in: Unit 10: Infinite Sequences and Series (BC)