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Chapter 5: Q. 48 (page 478)

Use limits of definite integrals to calculate each of the improper integrals in Exercises 21鈥�56.

鈭�1鈭�1xlnxdx

Short Answer

Expert verified

The value is鈭�.

Step by step solution

01

Step 1. Given information.

The given integral is鈭�1鈭�1xlnxdx.

02

Step 2. Value of the integral.

On simplifying,

Letu=ln(x)i.edu=1xdx鈭�1xln(x)dx=鈭�1udu=ln|u|Therefore,鈭�1鈭�1xlnxdx=limz鈫�0鈭�1B1xlnxdx=limB鈫�鈭�[ln|ln(x)|]1B=12limB鈫�鈭�[ln|ln(B)|-ln|ln(1)|]=12limB鈫�鈭�[ln|ln(B)|-ln|0|]=鈭�(Diverges)

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