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p-Integral Test for Improper Integrals
Worksheet
Grade Level
Calculus II
CAL2.48 p-Integral Test for Improper Integrals
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Use p-integral behavior to classify ∫_0^∞ x
2
/(1 + x
5
) dx.
A
Diverges; the numerator x
2
grows without bound.
B
Converges; near 0 it behaves like x
2
, and at infinity it behaves like 1/x
3
.
C
Diverges; at infinity the p-value is 1/3.
D
Cannot be classified because the integrand is a rational function.
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