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Calculus II
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Integral Test
Worksheet
Grade Level
Calculus II
CAL2.120 Integral Test
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For ∑_{n=2}
∞
1/[n(ln n)
3/4
], f(x)=1/[x(ln x)
3/4
] is positive, continuous, and decreasing for x≥ 2. What does the Integral Test conclude?
A
The series converges by the Integral Test because ∫_2
∞
1/[x(ln x)
3/4
] dx diverges.
B
The series diverges by the Integral Test because ∫_2
∞
1/[x(ln x)
3/4
] dx diverges.
C
The Integral Test proves convergence whenever the terms approach 0.
D
The Integral Test cannot be used because the terms are decreasing.
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