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Chapter 5: Q. 28 (page 478)

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

鈭�1鈭�x-1.01dx

Short Answer

Expert verified

The value of improper integrals is鈭�1鈭�x-1.01dx=100.

Step by step solution

01

Step 1. Given information.

The given improper integral is following.

鈭�1鈭�x-1.01dx

02

Step 2. Value of integral.

Write the integral in the proper form of鈭�1鈭�1xpdx

鈭�1鈭�1xpdx=鈭�1鈭�x-1.01dx鈭�1鈭�1xpdx=鈭�1鈭�1x1.01dxp=1.01&1.01>1

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

鈭�1鈭�x-1.01dx=limb鈫�鈭�鈭�1bx-1.01dx=limb鈫�鈭�-100x-0.011b=limb鈫�鈭�-100b-0.01+100=100

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Most popular questions from this chapter

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

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Find three integrals in Exercises 39鈥�74 that can be solved without using trigonometric substitution.
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