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Chapter 5: Q. 55 (page 478)

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

鈭�02x-2x(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�02x-2x(x-1)dx.

02

Step 2. Value of the integral.

On simplifying,

鈭�x-2x(x-1)dx=鈭�-1x-1+2xdx=鈭�2xdx-鈭�1x-1dx=2ln(|x|)-ln(|x-1|)鈭�02x-2x(x-1)dx=鈭�01x-2x(x-1)dx+鈭�12x-2x(x-1)dx=limA鈫�0[2ln(|x|)-ln(|x-1|)]A1+[2ln(|x|)-ln(|x-1|)]12=鈭�

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