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If \(f(x)=2\ln(\sqrt{e^x})\), what is the area bounded by f(x) for the interval [0, 2] on the x-axis?
Explanation:\(y=f(x)=2\ln(\sqrt{e^x})\)The area bounded by the curve y = f(x) and in the interval where x ? (0, 2) is given by:\(A=\int_0^22\ln(\sqrt{e^x})dx\)\(A=\int_0^22\ln({e^{x/2}})dx\)\(A=\int_0^22\times \frac{x}{2}dx\)\(A=\left[\frac{x^2}{2}\right]_0^2=[2-0]=2\)
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