$\int_{0}^{\frac{1}{2}}\frac{1}{\left(1-x\right)}dx$ এর মান কত?

The integral of $\frac{1}{1-x}$ is $-\ln|1-x|$ . Evaluating this from $0$ to $\frac{1}{2}$ : $[ -\ln|1-x| ]_{0}^{\frac{1}{2}} = -\ln|1-\frac{1}{2}| - (-\ln|1-0|)$ $= -\ln|\frac{1}{2}| + \ln|1|$ $= -\ln(\frac{1}{2}) + \ln(1)$ Since $\ln(1) = 0$ , we have: $= -\ln(\frac{1}{2})$ Using the property of logarithms $\ln(\frac{a}{b}) = -\ln(\frac{b}{a})$ : $= \ln(2)$ সুতরাং, সঠিক উত্তর হলো $\ln 2$ .