Flashcards
C6: Definitions
Cards in this deck (6)
- 1Integrated over Unbounded Intervals condition 1Let f be a function and a,b ∈ R, then (a) If f be continuous on [a,∞), then
∞
∫ f(x)dx
a = limR→∞
R
[∫ f(x)dx]
a - 2Integrated over Unbounded Intervals condition 2Let f be a function and a,b ∈ R, then
(b) If f is continuous on (−∞,b], then
b
∫ f(x)dx
−∞
= limL→∞
b
[∫ f(x)dx]
−L - 3Integrated over Unbounded Intervals condition 3Let f be a function and a,b ∈ R, then
If f be continuous on (−∞,∞), then we define, for any real number c,
∞
∫ f(x)dx
−∞
= lim
L→∞
c
[∫ f(x)dx]
−L
+ lim
R→∞
R
[∫ f(x)dx]
c - 4Integrating Unbounded Integrands Condition 1Let f be a function and a,b ∈ R, then
If f be continuous on (a,b] but not at x = a, then
b
∫ f(x)dx
a
= limε→0+
b
[∫ f(x)dx]
a+ε - 5Integrating Unbounded Integrands Condition 2Let f be a function and a,b ∈ R, then
If f is continuous on [a,b) but not at x = b, then
b
∫ f(x)dx
a
= limδ→0+
b−δ
[∫ f(x)dx]
a - 6Integrating Unbounded Integrands Condition 3Let f be a function and a,b ∈ R, then
If f is continuous on [a,c) ∪ (c,b] but not at x = c, then we define
b
∫ f(x)dx
a
= lim
δ→0+
c−δ
[∫ f(x)dx]
a
+ lim
ε→0+
b
[∫ f(x)dx]
c+ε
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- Calculus (Chapter 6: Applications & Techniques for Integration) Flashcards on C6: Definitions, created by Luke Danaher on 29/12/2016.
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- Luke Danaher
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