Evaluating Improper Integrals
AP Calculus BC · Flashcards · Recall
AP CALCULUS BC · FLASHCARDS
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QUESTION
State the condition for the convergence of
∫
0
a
(
a
−
x
)
−
1
/
2
d
x
\int_{0}^{a} (a-x)^{-1/2} \, dx
∫
0
a
(
a
−
x
)
−
1/2
d
x
.
QUESTION
What does it mean if an improper integral converges?
QUESTION
When does an integral
∫
a
b
f
(
x
)
d
x
\textstyle \int_{a}^{b} f(x) \, dx
∫
a
b
f
(
x
)
d
x
become improper?
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ANSWER
If
a
a
a
,
b
b
b
, or
f
(
x
)
f(x)
f
(
x
)
are infinite or unbounded. Any infinite bound or unbounded integrand makes it improper.
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