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Chapter 5: Q. 22 (page 478)

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

鈭�1鈭�1x34dx

Short Answer

Expert verified

The improper integrals on [0,鈭�)diverges.

鈭�1鈭�1x34dx=鈭�

Step by step solution

01

Step 1. Given information.

The given improper integral is following.

鈭�1鈭�1x34dx

02

Step 2. Value of integral.

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

localid="1648833762549" 鈭�1鈭�1xpdx=鈭�1鈭�1x34dx鈭�1鈭�1xpdx=鈭�1鈭�1x34dxp=34&34<1

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

鈭�1鈭�1x34dx=limb鈫�鈭�鈭�1b1x34dx=limb鈫�鈭�4x141b=limb鈫�鈭�4b14-4=鈭�

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