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# Workshop - The two funcions f(x and g(x are graphed on the...

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The two funcions f(x) and g(x) are graphed on the function above. Because g(x) is greater than f(x) from 0 to infinity, as shown in the graph, the area between g(x) and f(x) is the integral from the lower bound (a) to the upper bound (b) of g(x) – f(x) dx. . In this case, b approaches infinity, so the integral is improper.

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As the integral that is to be evaluated is an improper one, the upper bound of infinity is set to equal the arbitrary letter ‘R’. As a result of setting the upper bound equal to the arbitrary letter ‘R’, it is necessary to find the limit as R approaches infinity of (g(x) – f(x))dx from 0 to R. The functions of g(x) and f(x) are respectively substituted in (g(x) – f(x))dx from 0 to R , as, g(x) = (1 + e -x ) 2 and f(x) = (1 + e -2x ) 2 . After substituting the respective functions to procure a new integral, the integral must be simplified. Within the integral, (1+e -x ) 2 and (1 + e -2x ) 2 are multiplied out into 1 + 2e -x + e -2x and 1 + 2e -2x +e -4x , respectively. The subtraction of 1 + 2e
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Workshop - The two funcions f(x and g(x are graphed on the...

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