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Use limits of definite integrals to calculate each of the improper integrals in Exercises.

11x-22dx

Short Answer

Expert verified

The improper integral 11x-22dxdiverges.

Step by step solution

01

Step 1. Given information. 

The given integral is the following.

11x-22dx

02

Step 2. Value of integral. 

The function f(x)=1x-22has a vertical asymptote atx=2.

solve this improper integral by splitting at x=2

role="math" localid="1648878472203" 11x-22dx=121x-22dx+21x-22dx

Take role="math" localid="1648878379284" 121x-22dx

role="math" localid="1648878372798" 021x-22dx=limb0b21x-22dx=limb01x-2b2=limb01/0-1b-2=10+12=undefined

Integral 121x-22dxis undefined and diverges.

So integral 11x-22dxis also diverged.

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