The area bounded by the curve y = log x,the x | vedclass

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(C) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by $A = \int_{a}^{b} |f(x)| \, dx$.Given $y =

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$(\log 4 - 1) 	ext{ sq. units}$

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(C) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by $A = \int_{a}^{b} |f(x)| \, dx$.Given $y = \log x$,$x = 1$,and $x = 2$.Since $\log x > 0$ for $x \in [1, 2]$,the area is $\int_{1}^{2} \log x \, dx$.Using integration by parts,$\int \log x \, dx = x \log x - x + C$.Thus,$A = [x \log x - x]_{1}^{2}$.$A = (2 \log 2 - 2) - (1 \log 1 - 1)$.Since $\log 1 = 0$,$A = 2 \log 2 - 2 + 1 = 2 \log 2 - 1$.Using the property $n \log m = \log(m^n)$,$2 \log 2 = \log(2^2) = \log 4$.Therefore,$A = (\log 4 - 1) 	ext{ sq. units}$.

The area bounded by the curve $y = \log x$,the $x$-axis,and the ordinates $x = 1$ and $x = 2$ is:

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