Q. 1TF

Question

Improper Integrals: Determine whether the following improper integrals converge or diverge.

$\int_{1}^{\infty} \frac{1}{x} d x .$

Step-by-Step Solution

Verified

Answer

It is the divergent series.

1Step 1. Given Information.

$G i v e n a s e r i e s : \int_{1}^{\infty} \frac{1}{x} d x .$

2Step 2. Solving the integral.

$\int_{1}^{\infty} \frac{1}{x} d x = {[\ln x]}_{1}^{\infty} = [\ln \infty - \ln 1] = \infty - 0 = \infty . T h e r e f o r e, t h e s e r i e s i s a d i v e r g e n t s e r i e s .$

Q. 89

Q. 2TF

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Q. 2TF

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Q. 3TF

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