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Integral Calculus

Integration

MMTS_Full_Test_16

Grade 12

Question:

$\displaystyle\int_0^1\ln\left(\dfrac{1}{x}-1\right)dx$

$0$

$1$

$-1$

$\ln 2$

Step-by-Step Solution

Key Concept: Use $x\to 1-x$ substitution: $\ln(1/(1-x)-1)=\ln(x/(1-x))$

$I=0$.

Correct Answer: 1