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

1x-0.99dx

Short Answer

Expert verified

The improper integral on [1,)diverges.

1x-0.99dx=

Step by step solution

01

Step 1. Given information.

The given improper integral is following.

1x-0.99dx

02

Step 2. Value of integral.

Write the integral in the proper form of 11xpdx

11xpdx=1x-0.99dx11xpdx=11x0.99dxp=0.99&0.99<1

The Fundamental Theorem of Calculus tells us that the improper integral on [1,)diverges.

1x-0.99dx=limb1bx-0.99dx=limb100x0.011b=limb100b0.01-100=

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