This Integral Calculus lecture (pdf file) introduces the students to the topic of a series convergence test called the Integral Test.

Sub-topics included are:

• Formal definition of the Integral Test (with geometric argument as to why it works)
• Definition of the p-series (with the proof that the p-series converges for p > 1 using the Integral Test)
• Estimating the sum of a series if the series can be shown to be convergent using the Integral Test (with the geometric argument as to why it works).

Plus: many examples regarding these topics throughout.

Typed in LaTeX for a beautiful and professional look.

For these same notes, together with the scaffolded version, click here.

For a worksheet on practicing the Integral Test (20 questions + answers), click here.

If you enjoyed this product, you may be interested in other lecture notes related to infinite series:

• Infinite Sequences
• Introduction to Infinite Series
• Comparison Test - Series Convergence Test
• Alternating Series Test - Series Convergence Test
• Absolute Convergence, Ratio Test, Root Test
• Power Series
• Power Series Representation
• Taylor and Maclaurin Series
• Complete List of Convergence Tests