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Why does it make sense that 11xpdx diverges when 0<p1 ? Consider how 1xp compares with 1x in this case.

Short Answer

Expert verified

The integral gives the indefinite result forp=1.

Step by step solution

01

Step 1. Given information.   

We are given,

11xpdx

The integral diverges when 0<p1.

02

Step 2. Comparing the integral

When the integral 11xpdxis solved in the interval 0<p1, it gives an result of .

As when p=1is considered in the interval.

Then the resulting integral is lnxwhere the interval [,1]is applied which gives the indefinite result.

That's why the result is diverges.

In this case, 1xpis equal to 1xwhen p=1.

So,

11xdx=[lnx]1x=ln-ln1=

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