Module 7_ APCalcBC 7-6 Improper Integrals.pptx - 7.6 Improper Integrals 1\/22 Do Now Evaluate 2 2x 4 lim 3 x\u00ae \u00a5 3x x 2 HW Review Improper Integrals \u2022

# Module 7_ APCalcBC 7-6 Improper Integrals.pptx - 7.6...

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7.6 Improper Integrals 1/22 Do Now Evaluate lim x ®¥ 2 x 2 - 4 3 x 3 + x - 2
HW Review
Improper Integrals Areas that are unbounded are represented by improper integrals An integral is improper if The interval of integration may be infinite (bound to infinity) The integrand may tend to infinity (vertical asymptote in the bounds)
Improper integral Assume f(x) is integrable over [a,b] for all b>a. The improper integral of f(x) is defined as The improper integral converges if the limit exists (and is finite) and diverges if the limit does not exist (or is infinite) f ( x ) dx a ¥ ò = lim R ®¥ f ( x ) dx a R ò
Ex Evaluate dx x 3 2 ¥ ò
Ex Determine whether converges or not dx x - ¥ - 1 ò
The p-integral For a > 0, if P > 1 The integral diverges if P <= 1 dx x P a ¥ ò = a 1 - p p - 1
Ex Evaluate xe - x dx 0 ¥ ò
Comparing Integrals