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Convergence and divergence of basic improper integrals: Determine whether each of the given improper integrals converges or diverges. For those that converge, give the exact solution of the integral.

11xpdx,p=1

Short Answer

Expert verified

The integral is divergent.

Step by step solution

01

Step 1. Given information.

Consider the given information.

11xpdx

02

Step 2. Solve the integral.

Solve the given integral by applying the power rule.

11xpdx=1x-pdx=x-p+1-p+11=11-p-p+1-1-p+1=Undefined

The intergal is divegent for p=1.

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