Evaluating Improper Integrals
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Evaluate:
\textstyle \text{∫}_{0}^{1} \frac{1}{\text{√}x} \text{dx}
.
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?
QUESTION
Determine convergence:
∫
0
∞
e
−
x
2
d
x
\int_{0}^{\infty} e^{-x^2} \, dx
∫
0
∞
e
−
x
2
d
x
.
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ANSWER
Converges. Gaussian integral converges due to exponential decay.
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