`int_1^2 (x/2 - 2/x) dx` Evaluate the integral

Textbook Question

Chapter 5, 5.4 - Problem 33 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Hello!

First find the indefinite integral,

`int(x/(2)-2/x)dx=int(x/2)dx-int(2/x)dx=(x^2)/4-2ln(x).`

Then substitute x from 1 to 2:

`(2^2/4-2ln(2))-(1^2/4-2ln(1))=1-2ln(2)-1/4=3/4-2ln(2) approx -0.636.`

 

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