First slide

Integration

Question

$\int_{0}^{1} \frac{x - 1}{x^{2} - 1} d x$

Moderate

A

$ℓ n (2)$
B

$ℓ$ n(6) – $ℓ$ n(3)
C

$ℓ$ n(3) – $ℓ$ n(6)
D

– $ℓ$ n(2)

Solution

$\begin{array}{l} \int_{0}^{1} \frac{x - 1}{x^{2} - 1} = \int_{0}^{1} \frac{x - 1}{(x + 1) (x - 1)} \\ = {\int_{0}^{1} \frac{1}{(x + 1)} d x = ℓ n (x + 1))}_{0}^{1} = ℓ n 2 \end{array}$

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