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Improper Integrals with Infinite Limits
Worksheet
Grade Level
Calculus II
CAL2.44 Improper Integrals with Infinite Limits
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Which choice has both the correct limit setup and convergence conclusion for ∫_1^∞ 3x
2
/(x
3
+ 1)
2
dx?
A
lim_{b→∞} ∫_1
b
3x
2
/(x
3
+1)
2
dx = ∞; diverges
B
lim_{b→∞} ∫_1
b
3x
2
/(x
3
+1)
2
dx = lim_{b→∞}(1/2 - 1/(b
3
+1)) = 1/2; converges
C
lim_{b→∞} ∫_1
b
3x
2
/(x
3
+1)
2
dx = 1; converges
D
lim_{b→1} ∫_1
b
3x
2
/(x
3
+1)
2
dx = 0; diverges
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