Question

The value of the integral ∫log[(1/x) – 1]dx for x ∈ [0, 1] is...... 

(a) 1 

(b) (1/2) 

(c) 0 

(d) 2

Answer 1

The correct option (c) 0   

Explanation:

I = ¹∫₀log[(1/x) – 1]dx 

= ¹∫₀log[(1 – x)/x]dx 

= ¹∫₀log(1 – x)dx – ¹∫₀log x ∙ dx 

= ¹∫₀log[1– (1 – x)]dx – ¹∫₀logxdx 

= ¹∫₀logxdx – ¹∫₀logxdx = 0.