Improper Integrals (8.8) Tedmond Kou Corey Young.

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Presentation transcript:

Improper Integrals (8.8) Tedmond Kou Corey Young

Overview There are two types of improper integrals: 1) A definite integral with limits to infinity.

Overview 2 2) A definite integral that contains a discontinuity within its limits. Discontinuity at point c c c = +

Tips and Tricks 1) Graph the function so that you know what it looks like. Example: f(x)=xe -x 2

Tips and Tricks 2 2) Identify the kind of function, then utilize specific integration techniques. Integration by Parts Trig Substitutions Partial Fractions u du substitution Split limit into two xe -x 2 dx

Basic Steps 1) Identify the type of improper integral. xe -x 2 dx Split into two and each one becomes a definite integral with limits to infinity

Basic Steps 2/3 2) Take the limit to the point of infinity or discontinuity. 3) Take the anti-derivative

Basic Step 4 4) Plug in the numbers to check if the function is convergent or divergent.

Comparative Theorem

Examples with walkthrough Definite integral with limits to infinity:

Diverges

Examples with walkthrough Definite integral with discontinuous integrand:

Examples with walkthrough Comparative Theorem: Determine if the following integral is convergent or divergent.