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Chapter 5: Q. 52 (page 478)

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

鈭�011x(x-1)dx

Short Answer

Expert verified

The answer is-鈭�.

Step by step solution

01

Step 1. Given information.

The given integral is鈭�011x(x-1)dx.

02

Step 2. Value of the integral.

鈭�011x(x-1)dx=limA鈫�0鈭�A11x(x-1)dx鈭�1x(x-1)dx=鈭�1x-1-1xdx=鈭�1x-1dx-鈭�1xdx=ln(|x-1|)-ln(|x|)鈭�011x(x-1)dx=limx鈫�1[ln(|x-1|)-ln(|x|)]-limx鈫�0[ln(|x-1|)-ln(|x|)]=-鈭�

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