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Chapter 5: Q 24. (page 495)

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.

鈭�011xpdx,for0<p<1

Short Answer

Expert verified

The obtained result is1-p+1.

Step by step solution

01

Step 1. Given information.

Consider the given integral,

鈭�011xpdx

02

Step 2. Solve the integral.

Solve the given integral by applying the power rule.

鈭�011xpdx=鈭�01x-pdx=x-p+1-p+101=11-p1-p+1-0-p+1=11-p

Thus, the given integral is converges in the given iterval.

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