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irina1246 [14]
3 years ago
11

How do you do this question?

Mathematics
1 answer:
Luda [366]3 years ago
8 0

Answer:

∫ₑ°° 1 / (x (ln x)¹⁰) dx

∫₁°° x⁻³ dx

Step-by-step explanation:

A p-series 1 / xᵖ converges if p > 1.

∫ₑ°° 1 / (x (ln x)¹⁰) dx

If u = ln x, then du = 1/x dx.

When x = e, u = 1.  When x = ∞, u = ∞.

= ∫₁°° 1 / (u¹⁰) du

p = 10, converges

∫₁₀°° x^(-⅔) dx

= ∫₁₀°° 1 / (x^⅔) dx

p = ⅔, diverges

∫₁°° 2 / x^0.5 dx

= 2 ∫₁°° 1 / x^0.5 dx

p = 0.5, diverges

∫₁°° x⁻³ dx

= ∫₁°° 1 / x³ dx

p = 3, converges

∫₂°° 1/(3x) dx

= ⅓ ∫₂°° 1/x dx

p = 1, diverges

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